Let $G$ be a group and let $H$ be a subgroup of $G$.

$H$ is a **normal** subgroup of $G$ if and only if:

$gH=Hg$, for all $g\in G$

Denote:

by ${\rm GL}(2,{\mathbb R})$ the group of $2\times 2$ matrices with non-zero determinant

by ${\rm SL}(2,{\mathbb R})$ the group of $2\times 2$ matrices with determinant equal 1

Which of the following are true?