Invertible Matrix to Higher power I'm working on showing if A is invertible, that for any positive integer $n$, $(AMA^{-1})^n=(AM^nA^{-1})$
My first idea is induction on $n$ but is there a property of $A$ that explans why its power remains 1 or -1? Thanks in advance.

Hint: $AA^{-1}=A^{-1}A=I$ where $I$ is the identity matrix. Induction would be a good idea.
