Definition:Self-Inverse Element

Definition
Let $\left({S, \circ}\right)$ be a monoid whose identity element is $e$.

Then an element $a \in S$ is called self-inverse iff:
 * $x \circ x = e$.

That is, if $x = x^{-1}$, where $x$ is the inverse of $x$.

The definition is usually made in the context of a group.