Inverse Elements of Right Transversal is Left Transversal

Theorem
Let $G$ be a group.

Let $H$ be a subgroup of $G$.

Let $S \subseteq G$ be a right transversal for $H$ in $G$.

Let $T$ be the set defined as:


 * $T := \set {x^{-1}: x \in S}$

where $x^{-1}$ is the inverse of $x$ in $G$.

Then $T$ is a left transversal for $H$ in $G$.