Intersection and sums of subspaces

In the space $M$ of $2 \times 2$ matrices, the canonical basis is:$$E_{11} = \begin{bmatrix}1&0\\0&0\end{bmatrix}, \quad E_{12} = \begin{bmatrix}0&1\\0&0\end{bmatrix}, \quad E_{21} = \begin{bmatrix}0&0\\1&0\end{bmatrix}, \quad E_{22} = \begin{bmatrix}0&0\\0&1\end{bmatrix}$$Select the false statement.