1. IF matrices A, B and C are such that $\displaystyle A = B^{-1} C$ , Show that the inverse of $\displaystyle C^{-1}B$ is A

2. In this question i was given 2 matrices A and B . it tells me to work out AB which i know how to do, and then it says hence determine B.

how do i find the inverse of B from the product AB, im thinking i have to use I somewhere, do i make AB = I ?

i would appreciate if you can contribute your thinking process aswell. Im pretty good at all the matix calculations but when i see non standard questions like these which requres thinking, i just don't know where to start from and it really kills my confidence

Thanks!