diff --git a/lib/matrix.gi b/lib/matrix.gi
index f6f70c8c3a..0214cd15d9 100644
--- a/lib/matrix.gi
+++ b/lib/matrix.gi
@@ -1280,9 +1280,19 @@ InstallOtherMethod( ConstructingFilter,
     v -> IsPlistRep );
 
 InstallOtherMethod( BaseDomain,
-    "generic method for a matrix that is a plain list",
+    "generic method for a plain list matrix",
     [ IsMatrix and IsPlistRep ],
-    mat -> BaseDomain( mat[1] ) );
+    mat -> BaseDomain( Concatenation( mat ) ) );
+
+InstallOtherMethod( BaseDomain,
+    "generic method for a plain list matrix over a finite field",
+    [ IsMatrix and IsPlistRep and IsFFECollColl ],
+    DefaultFieldOfMatrix );
+
+InstallOtherMethod( BaseDomain,
+    "generic method for a plain list over the cyclotomics",
+    [ IsMatrix and IsPlistRep and IsCyclotomicCollColl ],
+    DefaultFieldOfMatrix );
 
 InstallOtherMethod( OneOfBaseDomain,
     "generic method for a matrix that is a plain list",
diff --git a/tst/testinstall/MatrixObj/BaseDomain.tst b/tst/testinstall/MatrixObj/BaseDomain.tst
new file mode 100644
index 0000000000..aad598888f
--- /dev/null
+++ b/tst/testinstall/MatrixObj/BaseDomain.tst
@@ -0,0 +1,62 @@
+gap> START_TEST("BaseDomain.tst");
+
+#
+gap> m := [[1,2],[3,4]];;
+gap> BaseDomain(m);
+Rationals
+gap> BaseDomain(Matrix(m));
+Rationals
+gap> BaseDomain(Matrix(Rationals, m));
+Rationals
+gap> BaseDomain(Matrix(Integers, m));
+Integers
+
+# FIXME: BUG:
+#gap> BaseDomain(Matrix(GF(2), m));
+#Rationals
+
+#
+gap> m := [[1,2],[3,4/3]];;
+gap> BaseDomain(m);
+Rationals
+gap> BaseDomain(Matrix(m));
+Rationals
+gap> BaseDomain(Matrix(Rationals, m));
+Rationals
+
+# FIXME: BUG:
+# gap> BaseDomain(Matrix(Integers, m));
+#Integers
+#gap> BaseDomain(Matrix(GF(2), m));
+#Rationals
+
+#
+gap> m := [[1,2],[3,4]] * Z(2);;
+gap> BaseDomain(m);
+GF(2)
+gap> BaseDomain(Matrix(m));
+GF(2)
+gap> BaseDomain(Matrix(GF(2), m));
+GF(2)
+
+# FIXME: BUG:
+#gap> BaseDomain(Matrix(Rationals, m));
+#Rationals
+
+#
+gap> m := [[1,2],[3,Z(4)]] * Z(2);;
+gap> BaseDomain(m);
+GF(2^2)
+gap> BaseDomain(Matrix(m));
+GF(2^2)
+gap> BaseDomain(Matrix(GF(4), m));
+GF(2^2)
+gap> BaseDomain(Matrix(GF(2), m));
+Error, ConvertToVectorRepNC: Vector cannot be written over GF(2)
+
+# FIXME: BUG:
+#gap> BaseDomain(Matrix(Rationals, m));
+#Rationals
+
+#
+gap> STOP_TEST("BaseDomain.tst");
diff --git a/tst/testinstall/grpreps.tst b/tst/testinstall/grpreps.tst
index e25c206041..859e2d15f6 100644
--- a/tst/testinstall/grpreps.tst
+++ b/tst/testinstall/grpreps.tst
@@ -18,4 +18,3 @@ gap> List( res2[2], r -> [ r.field, r.dimension ] );
 
 #
 gap> STOP_TEST( "grpreps.tst" );
-