[Solved] Another Group Theory problem...

This time, it's about proving 2 elements have the same order:-

*Let G be a group and x be an element of G. The ***order** of x is the least positive number such that * = e.. That is, n *__>__ 1 satisfies

* = e and * * =/= e for all 1*__<__m<n

For x in G prove that x and x^{-1} have the same order.

So, I've had a fair whack at the question, but I'm not sure if I'm going in the write direction.

. = = e

= e

=

=

=

=1 ---> e (identity is 1)

= e

Note: =

Therefore,

THUS. If

= 1 = e

= 1 = e

= 1 = e

=

Therefore they have the same order.

That is huge im sorry, but yeh. I dunno if it's correct. Any pointers?