the equation a⁻¹ * b * c * c⁻¹ * a * b⁻¹ * a * a⁻¹ = 1 isn't true in general (it simplifies to a⁻¹ * b * a * b⁻¹).
the equation a⁻¹ * b * c * c⁻¹ * a * b⁻¹ * a * a⁻¹ = 1 isn't true in general (it simplifies to a⁻¹ * b * a * b⁻¹).