Show that the dihedral group $D_n$ is isomorphic to a matrix group where all entries in the matrix are in $\Bbb{Z}_n$.

Question

The matrix group is

$$\left[\begin{matrix} \pm1 & k \\ 0 & 1 \end{matrix}\right], k\in\mathbb Z_n.$$

I know the properties of $D_n$ are that $r^n= e, s^2=e$ and $srs=r^{-1}$ for $r,s \in D_n$. But how do we use these properties to show they are isomorphic