A) \[AB=O,BA=O\]
B) \[AB=O,BA\ne O\]
C) \[AB\ne O,BA=O\]
D) \[AB\ne O,BA\ne O\]
Correct Answer: B
Solution :
\[AB=\,\left[ \begin{matrix} 1 & 0 \\ 2 & 0 \\ \end{matrix}\, \right]\,\left[ \begin{matrix} 0 & 0 \\ 1 & 12 \\ \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]=O\] while\[BA=\left[ \begin{matrix} 0 & 0 \\ 1 & 12 \\ \end{matrix} \right]\,\left[ \begin{matrix} 1 & 0 \\ 2 & 0 \\ \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 \\ 25 & 0 \\ \end{matrix} \right]\,\ne O\].
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