Subgroup of Index 2 is Normal

Subgroup of Index 2 is Normal: Let $G$ be a group and let $H\le G$ be a subgroup . If the index of $H$ in $G$ is $2$, then $H$ is normal in $G$.

Equivalently: if there are exactly two left cosets of $H$ in $G$, then the left cosets equal the right cosets, so $gH=Hg$ for all $g\in G$.