# Math Help - Simplifying matrices

1. ## Simplifying matrices

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

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

My attempt:
First I expanded $A^2$ to $AA$:
$AA(B^{-1}CA)^{-1}B^{-1}C^T$

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

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

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

$AC^{-1}C^T$

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!

2. Looks great! I don't think you can do anything more, unless you happen to know before-hand that C is unitary.

3. Thanks for the quick reply.

4. You're welcome. Have a good one!