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

Let G be a group and x be an element of G. Theorderof 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?