Thread: Matrix Power

If AB = BA and p is a nonnegative integer, prove that (AB)^ p = A^p B^p.

I've been sitting on this one for an hour and I'm just ridiculously confused!

Originally Posted by Brokescholar

If AB = BA and p is a nonnegative integer, prove that (AB)^ p = A^p B^p.

I've been sitting on this one for an hour and I'm just ridiculously confused!

by induction over p. if p = 1 it's clear. assuming it's true for p, then:

Awesome! You're a genius thanks for the help!