$GL(2,R) / SL(2,R)$ isomorphic to R* I am needing to write a prove showing that $GL(2,\mathbb{R}) / SL(2,\mathbb{R}) $ is isomorphic to $\mathbb{R}^*$.
I know that $SL(2,\mathbb{R})$ is a normal subgroup of $GL(2,\mathbb{R})$ but I'm not sure how to use that or where I should start.
Any help would be appreciated. Thanks.

The homomorphism $GL(2,\Bbb R)\to\Bbb R^*$, $A\mapsto \det A$ has $SL(2,\Bbb R)$ as kernel.
