# If the inverse of A^2 is B, how do you show that the inverse of A is AB?

If $B$ is the inverse of ${A}^{2}$
then $\left(A \times A\right) \times B = I$ (Definition of Inverse)
and $A \times \left(A \times B\right) = I$ (Associate Property)
$\Rightarrow \left(A \times B\right)$ is the inverse of $A$ (Definition of Inverse)