Lena W.

asked • 06/14/15

Group axioms proof

A group is a collection G that satisfies the following 3 axioms:

1) associativity a·(b·c)= (a·b)·c
2) identity element e: e·a=a ∀a in G
3) Inverse. Each element a in G has an inverse a-1 such that a-1·a=e

I want to prove that these three are sufficient to get a·e=a and a·a-1=e but insufficient to get a·a-1=e alone

If anyone can help me in steps that would be appreciated :)

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