a, b are in group G. Show o(ab) = o(ba).
I'm stumped. This would be trivial if G were abelian, but it's not. Please help.
EDIT: The back of the book has:
o(ab) = m
=> (ba)^m = (a^-1)(a)(ba)^m
= (a^-1)(ab)^m(a) (**)
I have NO clue how they got the step marked by (**).