Proving Invertible Matrix Property: kth Power

[ephemeral1]

Homework Statement

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

Homework Equations

none

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.

 

[vela]

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