Vector Spaces & Bases · Medium problem

Let $A = \begin{pmatrix}1 & 2\\2 & 4\end{pmatrix}$ and $B = \begin{pmatrix}1 & -1\\-1 & 1\end{pmatrix}$, both singular. This shows the singular $2\times 2$ matrices do NOT form a subspace of $M_2(\mathbb{R})$. What is $\det(A+B)$?