Let G be a group and let a, b 2 G. Show that (ab)n = anbn for all positive integers n
if and only if ab = ba.
---> Use a2b2 = (ab)2 = (ab)(ab) to show ab = ba. <---- Use induction.
I kinda get the forwards proof, but don't get the the back wards proof.
We want to show (ab)^n=a^nb^n
I don't see how we use induction for this.
Assume true for k=n
Show true for (ab)^(k+1)