Talk:1.1.7/@comment-74.69.51.122-20120605012413

The direction is not correct for your induction step--it's backwards. It needs to be A^{p+1} = AA^p = ... = (formula you found).

It's only a minor mistake, but what you are doing is assuming that your formula is correct, then using it to prove something else--that A^{p+1} = A * A^p, but we already know that--which is not what we want.