The question:

Given that A, B and C are invertible n x n matrices, simplify

$\displaystyle A^2(B^{-1}CA)^{-1}B^{-1}C^T$

My attempt:

First I expanded $\displaystyle A^2$ to $\displaystyle AA$:

$\displaystyle AA(B^{-1}CA)^{-1}B^{-1}C^T$

Then I found the inverse of the matricies within the parenthesis:

$\displaystyle AAA^{-1}C^{-1}BB^{-1}C^T$

$\displaystyle AA^{-1} $and $\displaystyle BB^{-1}$ are just I (the identity matrix) and can be removed:

$\displaystyle AC^{-1}C^T$

Does this look correct? My text has no solution for this question. I'm trying to think if I can do something with the C matrices.

Thanks!