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1.In proving that a set is a group from definition, we have to show there is an inverse element for each element, do we have to showuniquenessof it?

I believe this is unnecessary but people do this all the time.

My argument:

"For each [itex]a\in G[/itex], there exists a left inverse a' in G such that a'a=e." is enough.

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# How to prove that a set is a group? related difficult/challenge quesyion.

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