Describe the smallest subspace of $M_{2\times 2}$ that contains matrices
$\begin{bmatrix}2&1\\0&0\end{bmatrix},\begin{bmatrix}1&0\\0&2\end{bmatrix},\begin{bmatrix}0&-1\\0&0\end{bmatrix}\;.$
Find the dimension of this subspace.
It sounds like I would find the basis. I know how to do this with vectors, but how do I do this with a set of matrices?