Definition:Involution (Mapping)/Definition 3

Definition
Let $A$ be a set. Let $f: A \to A$ be a mapping on $A$.

Then $f$ is an involution $f$ is both a bijection and a symmetric relation.

That is, $f$ is a bijection such that $f = f^{-1}$.

Also see

 * Equivalence of Definitions of Involutive Mapping