Abelian implies every element is automorphic to its inverse

Statement
Suppose $$G$$ is an abelian group. Then, for any $$g \in G$$, there is an automorphism sending $$g$$ to $$g^{-1}$$.

Facts used

 * 1) uses::Inverse map is automorphism iff abelian

Proof
The proof follows from fact (1).