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

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 show

**uniqueness**of 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.