A possible mistake in a textbook about characterization of $\det(A+B)=0$ for $2 \times 2$ matrices

Question

If A and B are square matrices or order 2, then $\det(A + B) = 0$ is possible only when

1. $\det (A) = 0$ or $\det (B) = 0$

2. $\det (A) + \det (B) = 0$

3. $\det (A) = 0$ and $\det (B) = 0$

4. $A + B = 0$

Option D is said to be correct. But my doubt is:-

Suppose A = \begin{bmatrix}3&1\\2&6\end{bmatrix} and B = \begin{bmatrix}0&3\\4&2\end{bmatrix} Here the det (A+B) = 0. But none of the options are satisfied, not even the correct one. Am I right or am I missing something?