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: $\displaystyle (AB)^{p+1}=A(BA)^pB=A(AB)^pB=A(A^pB^p)B=A^{p+1}B^{ p+1}. \ \ \ \square$