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Question
If the matrix AB is zero, then
Options
It is not necessary that either A = O or, B = O
A = O or B = O
A = O and B = O
all the above statements are wrong
Solution
It is not necessary that either A = O or, B = O
\[ \text{Let A}= \begin{bmatrix}0 & 2 \\ 0 & 0\end{bmatrix} \text{and B}= \begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix}\]
\[ \therefore AB = \begin{bmatrix}0 & 2 \\ 0 & 0\end{bmatrix}\begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix} = \begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix}\]
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