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Question

If AB=O, then which of the following is always true


A

A=O

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B

B=O

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C

A and B need not be zero matrices

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D

A and B are zero matrices

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Solution

The correct option is C

A and B need not be zero matrices


Let us take A=[00a0] and B=[00b0].
Where a0 and b0
Now, AB
=[00a0][00b0]=[0000]
But none of A and B are zero matrices. So if AB is zero it is not necessary that either A=O or B=O.


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