A) \[A=O\] or \[B=O\]
B) \[A=O\] and \[B=O\]
C) It is not necessary that either \[A=O\]or \[B=O\]
D) \[A\ne O,B\ne O\]
Correct Answer: C
Solution :
\[AB=O\,\,\,\Rightarrow \,\,|AB|\,=\,0\] Þ \[|A|\,.\,|B|=0\] Þ \[|A|\,=\,0\] or \[|B|\,=\,0\] When AB = O, neither A nor B may be O. For example if \[A=\left[ \begin{matrix} 1 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] and\[B=\left[ \begin{matrix} 0 & 0 \\ 1 & 0 \\ \end{matrix} \right]\], then \[AB=\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]\].
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