# Linear Algebra

1. Feb 14, 2010

### ephemeral1

1. The problem statement, all variables and given/known data

Prove: If A is an invertible matrix and k is a positive integer, then
(A^k)^-1 = (A^-1)(A^-1) ....A^-1=(A^-1)^k

2. Relevant equations
none

3. The attempt at a solution

I have a hard time proving this. How do I go about doing this? Any help would be great. I really want to understand this. Thank you.

2. Feb 15, 2010

### vela

Staff Emeritus
Just multiply $A^k$ by $(A^{-1})^k$ and show you get the identity matrix.