If the matrix AB = O,then | vedclass

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(C) If $AB = O$,it does not necessarily imply that $A = O$ or $B = O$. For example,consider the matrices $A = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmat

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It is not necessary that either $A = O$ or $B = O$

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(C) If $AB = O$,it does not necessarily imply that $A = O$ or $B = O$. For example,consider the matrices $A = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 0 \ 1 & 0 \end{bmatrix}$. Calculating the product $AB$: $AB = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 0 \ 1 & 0 \end{bmatrix} = \begin{bmatrix} (1)(0) + (0)(1) & (1)(0) + (0)(0) \ (0)(0) + (0)(1) & (0)(0) + (0)(0) \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix} = O$. Here,$A 
e O$ and $B 
e O$,yet their product $AB = O$. Therefore,it is not necessary that either $A = O$ or $B = O$.

If the matrix $AB = O$,then

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