Answer:
Let \[A=\left[ \begin{matrix} 0 & 1 \\ 0 & 1 \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} 1 & 1 \\ 0 & 0 \\ \end{matrix} \right]\] Clearly, \[A\ne O\] and \[B\ne O\] Now, \[AB=\left[ \begin{matrix} 0 & 1 \\ 0 & 1 \\ \end{matrix} \right]\,\,\left[ \begin{matrix} 1 & 1 \\ 0 & 0 \\ \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] = O Hence proved.
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