Product_of_Commuting_Elements_with_Inverses

Let $x, y \in S$ such that $x$ and $y$ are both invertible. Then $x \circ y \circ x^{-1} \circ y^{-1} = e_S = x^{-1} \circ y^{-1} \circ x \circ y$ $x$ and $y$ commute.