If the matrix AB is zero, then

If $A=\begin{bmatrix}1&0\\0&0\end{bmatrix},B=\begin{bmatrix}0&0\\0&1\end{bmatrix}$, then $AB=\begin{bmatrix}0&0\\0&0\end{bmatrix}$

However, $A≠O, B≠O$.

So, option (1) is correct.