Definition:Self-Inverse Element/Definition 1

Definition
Let $\struct {S, \circ}$ be a monoid whose identity element is $e$.

Let $x \in S$ be an element of $S$.

$x$ is a self-inverse element of $\struct {S, \circ}$ $x \circ x = e$.

Also see

 * Equivalence of Definitions of Self-Inverse