$$S = \left\{
\begin{pmatrix}
2a && -b \\
3b && a
\end{pmatrix}\;:\;\; a,b \in \Bbb R\right\}$$

So, I have to find that it is either closed under addition and scalar multiplication, I asked a similar question to this earlier today but made a mistake with how I asked it, so apologies for that. However I am still left with a few difficulties in the proving that is/isn't a subspace of $M\_2(\mathbb{R})$ 

Also, can a set S be a subspace of $M\_2(\mathbb{R})$ at all? Or does it fail from the beginning?