Answer
See explanations.
Work Step by Step
Step 1. Let matrix A and B as:
$\begin{array}( \\A= \\ \\ \end{array}
\begin{bmatrix} a_1 &0\\a_2 &0 \end{bmatrix},
\begin{array}( \\B= \\ \\ \end{array}
\begin{bmatrix} 0 &0\\b_1 &b_2 \end{bmatrix} $
where $a_1\ne0, a_2\ne0, b_1\ne0, b_2\ne0,$
Step 2. Check $A\ne O, B\ne O$, but $AB=O$
Step 3. Let $a_2=b_1\ne0, a_1=b_2=0$, we have $A\ne O$ and $AB=A^2=O$
Step 4. There are other cases by considering the symmetry of the matrices.
