Condition for Subset of Group to be Right Transversal

Theorem
Let $G$ be a group.

Let $H$ be a subgroup of $G$ whose index in $G$ is $n$:
 * $\index G H = n$

Let $S \subseteq G$ be a subset of $G$ of cardinality $n$.

Then $S$ is a right transversal for $H$ in $G$ :
 * $\forall x, y \in S: x \ne y \implies x y^{-1} \notin H$