On the edge of completing this proof about the order of an element

[jdinatale]

Homework Statement

The Attempt at a Solution

Based on my attempt above, I have demonstrated that the order is less than or equal to n. I am certain that it is actually n, but I'm not sure which theorem I can grab finish this thing off. Any tips for pointing me in the right direction?

 

[Dick]

(bab^(-1))^m is equal to b*a^m*b^(-1) for any m. You've shown that. If that's equal to e for m<n, then was the order of a really n?