Question:
Given an example of two non-zero $2 \times 2$ matrices $A$ and $B$ such that $A B=O$.
Solution:
Let the two matrices be $A=\left[\begin{array}{ll}5 & 0 \\ 9 & 0\end{array}\right]$ and $B=\left[\begin{array}{cc}0 & 0 \\ 12 & -21\end{array}\right]$, such that $A B=\left[\begin{array}{ll}5 & 0 \\ 9 & 0\end{array}\right]\left[\begin{array}{cc}0 & 0 \\ 12 & -21\end{array}\right]$.
$\Rightarrow A B=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$