Inversion Mapping is Permutation/Proof 1

Theorem
Let $\left({G, \circ}\right)$ be a group.

Let $\iota: G \to G$ be the inversion mapping on $G$.

Then $\iota$ is a permutation on $G$.

Proof
The inversion mapping on $G$ is the mapping $\iota: G \to G$ defined by:


 * $\forall g \in G: \iota \left({g}\right) = g^{-1}$

where $g^{-1}$ is the inverse or $g$.

By Inversion Mapping is Involution, $\iota$ is an involution:
 * $\forall g \in G: \iota \left({\iota (g)}\right) = g$

The result follows from Involution is Permutation.