I have to show that in a group G |ab|=|ba| for all a,b in G.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# |ab|=|ba| in a group

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