I have to show that in a group G |ab|=|ba| for all a,b in G. I don't have a clue how to proceed. I assume |ab|=n. I feel that using associativity, identity and inverse should be important. But I don't see how these tools will get me to |ba|=n. I've considered proof by contradiciton, but that doesn't seem to be useful here. Can someone please give me a hint?