Inverse of Commuting Pair

Theorem
Let $\struct {S, \circ}$ be a monoid whose identity is $e_S$. Let $x, y \in S$ such that $x$ and $y$ are both invertible.

Then $x$ commutes with $y$ :
 * $\struct {x \circ y}^{-1} = x^{-1} \circ y^{-1}$