diff --git a/.auto-claude-security.json b/.auto-claude-security.json
new file mode 100644
index 00000000..1712c7eb
--- /dev/null
+++ b/.auto-claude-security.json
@@ -0,0 +1,183 @@
+{
+  "base_commands": [
+    ".",
+    "[",
+    "[[",
+    "ag",
+    "awk",
+    "basename",
+    "bash",
+    "bc",
+    "break",
+    "cat",
+    "cd",
+    "chmod",
+    "clear",
+    "cmp",
+    "column",
+    "comm",
+    "command",
+    "continue",
+    "cp",
+    "curl",
+    "cut",
+    "date",
+    "df",
+    "diff",
+    "dig",
+    "dirname",
+    "du",
+    "echo",
+    "egrep",
+    "env",
+    "eval",
+    "exec",
+    "exit",
+    "expand",
+    "export",
+    "expr",
+    "false",
+    "fd",
+    "fgrep",
+    "file",
+    "find",
+    "fmt",
+    "fold",
+    "gawk",
+    "gh",
+    "git",
+    "grep",
+    "gunzip",
+    "gzip",
+    "head",
+    "help",
+    "host",
+    "iconv",
+    "id",
+    "jobs",
+    "join",
+    "jq",
+    "kill",
+    "killall",
+    "less",
+    "let",
+    "ln",
+    "ls",
+    "lsof",
+    "man",
+    "mkdir",
+    "mktemp",
+    "more",
+    "mv",
+    "nl",
+    "paste",
+    "pgrep",
+    "ping",
+    "pkill",
+    "popd",
+    "printenv",
+    "printf",
+    "ps",
+    "pushd",
+    "pwd",
+    "read",
+    "readlink",
+    "realpath",
+    "reset",
+    "return",
+    "rev",
+    "rg",
+    "rm",
+    "rmdir",
+    "sed",
+    "seq",
+    "set",
+    "sh",
+    "shuf",
+    "sleep",
+    "sort",
+    "source",
+    "split",
+    "stat",
+    "tail",
+    "tar",
+    "tee",
+    "test",
+    "time",
+    "timeout",
+    "touch",
+    "tr",
+    "tree",
+    "true",
+    "type",
+    "uname",
+    "unexpand",
+    "uniq",
+    "unset",
+    "unzip",
+    "watch",
+    "wc",
+    "wget",
+    "whereis",
+    "which",
+    "whoami",
+    "xargs",
+    "yes",
+    "yq",
+    "zip",
+    "zsh"
+  ],
+  "stack_commands": [
+    "composer",
+    "ipython",
+    "jupyter",
+    "node",
+    "notebook",
+    "npm",
+    "npx",
+    "pdb",
+    "php",
+    "phpunit",
+    "pip",
+    "pip3",
+    "pipx",
+    "pudb",
+    "python",
+    "python3"
+  ],
+  "script_commands": [
+    "./parallel.sh"
+  ],
+  "custom_commands": [],
+  "detected_stack": {
+    "languages": [
+      "python",
+      "javascript",
+      "php"
+    ],
+    "package_managers": [
+      "composer"
+    ],
+    "frameworks": [
+      "phpunit"
+    ],
+    "databases": [],
+    "infrastructure": [],
+    "cloud_providers": [],
+    "code_quality_tools": [],
+    "version_managers": []
+  },
+  "custom_scripts": {
+    "npm_scripts": [],
+    "make_targets": [],
+    "poetry_scripts": [],
+    "cargo_aliases": [],
+    "shell_scripts": [
+      "parallel.sh"
+    ]
+  },
+  "project_dir": "/home/jordan/Projects/Fermat",
+  "created_at": "2026-01-17T02:59:58.884479",
+  "project_hash": "ff04866add36ffa1116480549ed508fe",
+  "inherited_from": "/home/jordan/Projects/Fermat"
+}
\ No newline at end of file
diff --git a/.auto-claude-status b/.auto-claude-status
new file mode 100644
index 00000000..b5861a45
--- /dev/null
+++ b/.auto-claude-status
@@ -0,0 +1,25 @@
+{
+  "active": true,
+  "spec": "001-matrix-minors-and-cofactors",
+  "state": "building",
+  "subtasks": {
+    "completed": 6,
+    "total": 7,
+    "in_progress": 1,
+    "failed": 0
+  },
+  "phase": {
+    "current": "Add Comprehensive Tests",
+    "id": null,
+    "total": 3
+  },
+  "workers": {
+    "active": 0,
+    "max": 1
+  },
+  "session": {
+    "number": 1,
+    "started_at": "2026-01-17T17:25:02.226019"
+  },
+  "last_update": "2026-01-17T17:25:02.286953"
+}
\ No newline at end of file
diff --git a/.claude_settings.json b/.claude_settings.json
new file mode 100644
index 00000000..234ec972
--- /dev/null
+++ b/.claude_settings.json
@@ -0,0 +1,39 @@
+{
+  "sandbox": {
+    "enabled": true,
+    "autoAllowBashIfSandboxed": true
+  },
+  "permissions": {
+    "defaultMode": "acceptEdits",
+    "allow": [
+      "Read(./**)",
+      "Write(./**)",
+      "Edit(./**)",
+      "Glob(./**)",
+      "Grep(./**)",
+      "Read(/home/jordan/Projects/Fermat/.auto-claude/worktrees/tasks/001-matrix-minors-and-cofactors/**)",
+      "Write(/home/jordan/Projects/Fermat/.auto-claude/worktrees/tasks/001-matrix-minors-and-cofactors/**)",
+      "Edit(/home/jordan/Projects/Fermat/.auto-claude/worktrees/tasks/001-matrix-minors-and-cofactors/**)",
+      "Glob(/home/jordan/Projects/Fermat/.auto-claude/worktrees/tasks/001-matrix-minors-and-cofactors/**)",
+      "Grep(/home/jordan/Projects/Fermat/.auto-claude/worktrees/tasks/001-matrix-minors-and-cofactors/**)",
+      "Read(/home/jordan/Projects/Fermat/.auto-claude/worktrees/tasks/001-matrix-minors-and-cofactors/.auto-claude/specs/001-matrix-minors-and-cofactors/**)",
+      "Write(/home/jordan/Projects/Fermat/.auto-claude/worktrees/tasks/001-matrix-minors-and-cofactors/.auto-claude/specs/001-matrix-minors-and-cofactors/**)",
+      "Edit(/home/jordan/Projects/Fermat/.auto-claude/worktrees/tasks/001-matrix-minors-and-cofactors/.auto-claude/specs/001-matrix-minors-and-cofactors/**)",
+      "Read(/home/jordan/Projects/Fermat/.auto-claude/**)",
+      "Write(/home/jordan/Projects/Fermat/.auto-claude/**)",
+      "Edit(/home/jordan/Projects/Fermat/.auto-claude/**)",
+      "Glob(/home/jordan/Projects/Fermat/.auto-claude/**)",
+      "Grep(/home/jordan/Projects/Fermat/.auto-claude/**)",
+      "Bash(*)",
+      "WebFetch(*)",
+      "WebSearch(*)",
+      "mcp__context7__resolve-library-id(*)",
+      "mcp__context7__get-library-docs(*)",
+      "mcp__graphiti-memory__search_nodes(*)",
+      "mcp__graphiti-memory__search_facts(*)",
+      "mcp__graphiti-memory__add_episode(*)",
+      "mcp__graphiti-memory__get_episodes(*)",
+      "mcp__graphiti-memory__get_entity_edge(*)"
+    ]
+  }
+}
\ No newline at end of file
diff --git a/.gitignore b/.gitignore
index 9af31763..91fe11b2 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,10 +1,13 @@
-.idea
-vendor/
-composer.lock
-build
-.phpunit.result.cache
-site
-tools/
-.php-cs-fixer.cache
-.phive/
-phive.phar.asc
\ No newline at end of file
+.idea
+vendor/
+composer.lock
+build
+.phpunit.result.cache
+site
+tools/
+.php-cs-fixer.cache
+.phive/
+phive.phar.asc
+
+# Auto Claude data directory
+.auto-claude/
diff --git a/src/Samsara/Fermat/LinearAlgebra/Types/Matrix.php b/src/Samsara/Fermat/LinearAlgebra/Types/Matrix.php
index 207cf938..ff0bf0e7 100644
--- a/src/Samsara/Fermat/LinearAlgebra/Types/Matrix.php
+++ b/src/Samsara/Fermat/LinearAlgebra/Types/Matrix.php
@@ -59,7 +59,14 @@ public function getDeterminant(): ImmutableDecimal
             );
         }
 
-        if ($this->numRows > 2) {
+        if ($this->numRows === 0) {
+            // The determinant of a 0x0 matrix is defined as 1 by convention
+            $determinant = Numbers::makeOne();
+        } elseif ($this->numRows === 1) {
+            $determinant = $this->rows[0]->get(0);
+        } elseif ($this->numRows === 2) {
+            $determinant = $this->rows[0]->get(0)->multiply($this->rows[1]->get(1))->subtract($this->rows[1]->get(0)->multiply($this->rows[0]->get(1)));
+        } else {
             $determinant = Numbers::makeZero();
 
             foreach ($this->rows[0]->toArray() as $key => $value) {
@@ -67,8 +74,6 @@ public function getDeterminant(): ImmutableDecimal
 
                 $determinant = $determinant->add($value->multiply($childMatrix->getDeterminant())->multiply(SequenceProvider::nthPowerNegativeOne($key)));
             }
-        } else {
-            $determinant = $this->rows[0]->get(0)->multiply($this->rows[1]->get(1))->subtract($this->rows[1]->get(0)->multiply($this->rows[0]->get(1)));
         }
 
         return $determinant;
@@ -84,7 +89,6 @@ public function getInverseMatrix(): static
         $determinant = $this->getDeterminant();
         $inverseDeterminant = new ImmutableFraction(Numbers::makeOne(), $determinant);
 
-        // TODO: Implement minors & cofactors method https://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html
         if ($this->getRowCount() > 2) {
             $minors = $this->getMatrixOfMinors();
             $cofactors = $minors->applyAlternatingSigns();
@@ -114,6 +118,31 @@ public function getMatrixOfMinors(): static
         return $this->mapFuction($fn);
     }
 
+    /**
+     * Returns a new collection that contains the matrix of minors for each element in the current collection.
+     *
+     * This is an alias for getMatrixOfMinors().
+     *
+     * @return static A new collection containing the matrix of minors.
+     */
+    public function minors(): static
+    {
+        return $this->getMatrixOfMinors();
+    }
+
+    /**
+     * Returns a new matrix containing the cofactors of each element in the current matrix.
+     *
+     * The matrix of cofactors is obtained by taking the matrix of minors and applying alternating signs
+     * based on position. The sign pattern follows a checkerboard pattern starting with + at position (0,0).
+     *
+     * @return static A new matrix containing the cofactors.
+     */
+    public function cofactors(): static
+    {
+        return $this->getMatrixOfMinors()->applyAlternatingSigns();
+    }
+
     /**
      * Adds a MatrixInterface object to the current matrix and returns a new matrix with the sum.
      *
diff --git a/src/Samsara/Fermat/LinearAlgebra/Types/Traits/Matrix/ShapeTrait.php b/src/Samsara/Fermat/LinearAlgebra/Types/Traits/Matrix/ShapeTrait.php
index e2e70735..5397b060 100644
--- a/src/Samsara/Fermat/LinearAlgebra/Types/Traits/Matrix/ShapeTrait.php
+++ b/src/Samsara/Fermat/LinearAlgebra/Types/Traits/Matrix/ShapeTrait.php
@@ -30,11 +30,16 @@ public function getAdjoint(): static
     }
 
     /**
+     * Returns the adjugate matrix (also known as classical adjoint).
+     *
+     * The adjugate is the transpose of the cofactor matrix.
+     * This is different from getAdjoint() which is just the transpose.
+     *
      * @return static
      */
     public function getAdjugate(): static
     {
-        return $this->getAdjoint();
+        return $this->cofactors()->getAdjoint();
     }
 
     /**
diff --git a/tests/Samsara/Fermat/LinearAlgebra/Types/MatrixTest.php b/tests/Samsara/Fermat/LinearAlgebra/Types/MatrixTest.php
index b09966fa..138245fc 100644
--- a/tests/Samsara/Fermat/LinearAlgebra/Types/MatrixTest.php
+++ b/tests/Samsara/Fermat/LinearAlgebra/Types/MatrixTest.php
@@ -512,10 +512,10 @@ public function testAdjugate()
         $matrix = new ImmutableMatrix($matrixData);
         $adjugate = $matrix->getAdjugate();
 
-        $this->assertEquals('3', $adjugate->getRow(0)->get(0)->getValue());
-        $this->assertEquals('4', $adjugate->getRow(0)->get(1)->getValue());
-        $this->assertEquals('5', $adjugate->getRow(1)->get(0)->getValue());
-        $this->assertEquals('2', $adjugate->getRow(1)->get(1)->getValue());
+        $this->assertEquals('2', $adjugate->getRow(0)->get(0)->getValue());
+        $this->assertEquals('-5', $adjugate->getRow(0)->get(1)->getValue());
+        $this->assertEquals('-4', $adjugate->getRow(1)->get(0)->getValue());
+        $this->assertEquals('3', $adjugate->getRow(1)->get(1)->getValue());
 
     }
 
@@ -571,4 +571,98 @@ public function testShiftColumn()
         $this->assertEquals('4', $column->get(1)->getValue());
     }
 
+    public function testMinors()
+    {
+        // Test 2x2 matrix
+        $matrixData = [
+            new NumberCollection([Numbers::make(Numbers::IMMUTABLE, '3'), Numbers::make(Numbers::IMMUTABLE, '5')]), // row 1
+            new NumberCollection([Numbers::make(Numbers::IMMUTABLE, '4'), Numbers::make(Numbers::IMMUTABLE, '2')]), // row 2
+        ];
+
+        $matrix = new ImmutableMatrix($matrixData);
+        $minorMatrix = $matrix->minors();
+
+        $this->assertEquals('2', $minorMatrix->getRow(0)->get(0)->getValue());
+        $this->assertEquals('4', $minorMatrix->getRow(0)->get(1)->getValue());
+        $this->assertEquals('5', $minorMatrix->getRow(1)->get(0)->getValue());
+        $this->assertEquals('3', $minorMatrix->getRow(1)->get(1)->getValue());
+
+        // Test 3x3 matrix
+        $matrixData = [
+            new NumberCollection([new ImmutableDecimal(3), new ImmutableDecimal(0), new ImmutableDecimal(2)]),
+            new NumberCollection([new ImmutableDecimal(2), new ImmutableDecimal(0), new ImmutableDecimal(-2)]),
+            new NumberCollection([new ImmutableDecimal(0), new ImmutableDecimal(1), new ImmutableDecimal(1)])
+        ];
+
+        $matrix = new ImmutableMatrix($matrixData);
+        $minorMatrix = $matrix->minors();
+
+        $this->assertEquals('2', $minorMatrix->getRow(0)->get(0)->getValue());
+        $this->assertEquals('2', $minorMatrix->getRow(0)->get(1)->getValue());
+        $this->assertEquals('2', $minorMatrix->getRow(0)->get(2)->getValue());
+        $this->assertEquals('-2', $minorMatrix->getRow(1)->get(0)->getValue());
+        $this->assertEquals('3', $minorMatrix->getRow(1)->get(1)->getValue());
+        $this->assertEquals('3', $minorMatrix->getRow(1)->get(2)->getValue());
+        $this->assertEquals('0', $minorMatrix->getRow(2)->get(0)->getValue());
+        $this->assertEquals('-10', $minorMatrix->getRow(2)->get(1)->getValue());
+        $this->assertEquals('0', $minorMatrix->getRow(2)->get(2)->getValue());
+
+        // Test 1x1 matrix
+        $matrixData = [
+            new NumberCollection([Numbers::make(Numbers::IMMUTABLE, '5')])
+        ];
+
+        $matrix = new ImmutableMatrix($matrixData);
+        $minorMatrix = $matrix->minors();
+
+        $this->assertEquals('1', $minorMatrix->getRow(0)->get(0)->getValue());
+    }
+
+    public function testCofactors()
+    {
+        // Test 2x2 matrix
+        $matrixData = [
+            new NumberCollection([Numbers::make(Numbers::IMMUTABLE, '3'), Numbers::make(Numbers::IMMUTABLE, '5')]), // row 1
+            new NumberCollection([Numbers::make(Numbers::IMMUTABLE, '4'), Numbers::make(Numbers::IMMUTABLE, '2')]), // row 2
+        ];
+
+        $matrix = new ImmutableMatrix($matrixData);
+        $cofactorMatrix = $matrix->cofactors();
+
+        $this->assertEquals('2', $cofactorMatrix->getRow(0)->get(0)->getValue());
+        $this->assertEquals('-4', $cofactorMatrix->getRow(0)->get(1)->getValue());
+        $this->assertEquals('-5', $cofactorMatrix->getRow(1)->get(0)->getValue());
+        $this->assertEquals('3', $cofactorMatrix->getRow(1)->get(1)->getValue());
+
+        // Test 3x3 matrix
+        $matrixData = [
+            new NumberCollection([new ImmutableDecimal(3), new ImmutableDecimal(0), new ImmutableDecimal(2)]),
+            new NumberCollection([new ImmutableDecimal(2), new ImmutableDecimal(0), new ImmutableDecimal(-2)]),
+            new NumberCollection([new ImmutableDecimal(0), new ImmutableDecimal(1), new ImmutableDecimal(1)])
+        ];
+
+        $matrix = new ImmutableMatrix($matrixData);
+        $cofactorMatrix = $matrix->cofactors();
+
+        $this->assertEquals('2', $cofactorMatrix->getRow(0)->get(0)->getValue());
+        $this->assertEquals('-2', $cofactorMatrix->getRow(0)->get(1)->getValue());
+        $this->assertEquals('2', $cofactorMatrix->getRow(0)->get(2)->getValue());
+        $this->assertEquals('2', $cofactorMatrix->getRow(1)->get(0)->getValue());
+        $this->assertEquals('3', $cofactorMatrix->getRow(1)->get(1)->getValue());
+        $this->assertEquals('-3', $cofactorMatrix->getRow(1)->get(2)->getValue());
+        $this->assertEquals('0', $cofactorMatrix->getRow(2)->get(0)->getValue());
+        $this->assertEquals('10', $cofactorMatrix->getRow(2)->get(1)->getValue());
+        $this->assertEquals('0', $cofactorMatrix->getRow(2)->get(2)->getValue());
+
+        // Test 1x1 matrix
+        $matrixData = [
+            new NumberCollection([Numbers::make(Numbers::IMMUTABLE, '5')])
+        ];
+
+        $matrix = new ImmutableMatrix($matrixData);
+        $cofactorMatrix = $matrix->cofactors();
+
+        $this->assertEquals('1', $cofactorMatrix->getRow(0)->get(0)->getValue());
+    }
+
 }
diff --git a/vendor b/vendor
new file mode 120000
index 00000000..f42b6d55
--- /dev/null
+++ b/vendor
@@ -0,0 +1 @@
+/home/jordan/Projects/Fermat/vendor
\ No newline at end of file