Matrix Manifolds Question I am not sure at all how to do the following question.  Any help is appreciated.  Thank you.
Consider $SL_n \mathbb{R}$ as a group and as a topological space with
the topology induced from $R^{n^2}$. Show that if $H \subset  SL_n \mathbb{R}$ is an abelian subgroup, then the closure $H$ of $SL_n \mathbb{R}$ is also an abelian subgroup.

Hint: The map $\overline{H}\times \overline{H}\to \overline{H}$ defined by $(a,b)\mapsto aba^{-1}b^{-1}$ is continuous. Since $\overline{H}$ is Hausdorff, and the map is constant on a dense subset of its domain, it must be constant everywhere.
