
Vector subspace
Which of the following subsets of the vector space Mnn are subspaces?
The set of all nxn nonsingular matrices is not a subspace.
I don't get why it's not a subspace. I understand that if it's a zero matrix then it wouldn't be nonsingular. But how would I prove that it's not a subspace by using the two properties:
u + v
cu
Thanks!

$\displaystyle \left( {\begin{array}{lr}
1 & 0 \\
0 & 1 \\
\end{array}} \right) + \left( {\begin{array}{lr}
{  1} & 0 \\
0 & {  1} \\
\end{array}} \right) = ?$