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 $\mathbb{R}^4$?

If $A=(a_{ij})$ and $B=(b_{ij})$ then the inherited metric will be: $$d(A,B)=\sqrt{\sum_{i,j} (a_{ij}-b_{ij})^2}$$
no matter whether you associate $\begin{pmatrix}a&b\\c&d\end{pmatrix}$ with $(a,b,c,d)$, $(a,c,b,d)$ or any other re-ordering of the values.
