Inversion Mapping is Permutation/Proof 1

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


 * $\forall g \in G: \map \iota g = g^{-1}$

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

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

The result follows from Involution is Permutation.