Let (G,∗) be a binary structure that has the following properties:
1) The binary operation ∗ is associative.
2) There exists an element e∈G such that for all a∈G, e∗a=a (Existence of left Identity).
3) For all a∈G, there exists b∈G such that b∗a=e (existence of left inverses)
Prove that (G,∗) is a group.

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All you need to show, is that it also has a right identity, and a right inverse.

yea,,, I have hourssss trying to :(

That's true as well for non-Abelian groups, right?

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