Can anybody help me with this Abstract Algebra problem?

Question

It's a proof:

Let G be a group. Prove that the mapping alpha(g)=g^(-1) for all g in G is an automorphism if and only if G is Abelian.

Answer 1

Let a denote alpha, and consider
a(gh) = (gh)^(-1) =h^(-1)g^(-1).
But that is g^(-1)h^(-1) if and only if G is abelian.

Answer 2

OMG r u sure this is algebra? It looks like something not from my side of the universe.