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, i.e.:


 * $\forall g \in G: \iota \left({\iota (g)}\right) = g$

Proof
Let $g \in G$.

Then:

which establishes the result.