Question

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

Answer 1

Note that the Associative Property applies to matrix multiplication

Explanation:

If `B` is the inverse of `A^2`
then `(AxxA)xxB=I` (Definition of Inverse)
and `Axx(AxxB)=I` (Associate Property)
`rArr (AxxB)` is the inverse of `A` (Definition of Inverse)