Inverse of Inverse/Monoid

Corollary to Inverse of Inverse in Associative Structure
Let $\left({S, \circ}\right)$ be a monoid.

Let $x \in S$ be invertible, and let its inverse be $x^{-1}$.

Then $x^{-1}$ is also invertible, and:
 * $\left({x^{-1}}\right)^{-1} = x$

Proof
By definition, a monoid is an algebraic structure whose operation is associative.

The result follows by Inverse of Inverse in Associative Structure.