Inversion Mapping is Involution

Theorem
Let $G$ be a group, and let $\iota: G \to G$ be the inversion mapping.

Then $\iota$ is an involution, that is:


 * $\forall g \in G: \map \iota {\map \iota g} = g$

Proof
Let $g \in G$.

Then:

which establishes the result.