Definition:Self-Inverse Element

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

Then an element $x \in S$ is called self-inverse :


 * $x \circ x = e$

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

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

Also see

 * Equivalence of Definitions of Self-Inverse