Left and Right Cosets of a Subgroup of Index 2 Show that if $H$ is a subgroup of index $2$ in a finite group $G$, then every left coset of $H$ is also a right coset of $H$.
$H$ is a coset, and the only other possible coset is $G \setminus H$ by order considerations.
$H$ is a coset, and the only other possible coset is $G \setminus H$ by order considerations.