Subspace topology of matrices I have been given homework in which the $2\times 2$ matrices of determinant $1$ are equipped with the subspace topology of $\mathbb{R}^4$. However, $\mathbb{R}^4$ is a space of 4-tuples, while 2x2 matrices are not n-tuples. How do I get the open sets of this topology?
How is this set of matrices a subset of $\mathbb{R}^4$?

Any matrix 
$$\begin{pmatrix}
a & b\\
c & d
\end{pmatrix}\in\mbox{Mat}^{2\times 2}(\mathbb{Z})$$
can be interpreted as the touple $(a,b,c,d)\in\mathbb{R}^4$, so $\mbox{Mat}^{2\times 2}(\mathbb{Z})$ can be thought of a subspace of $\mathbb{R}^4$ and be given the subspace topology.
