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If A and B are two nonzero square matric...

If A and B are two nonzero square matrices of the same order such that the product `AB=O`, then

A

both A and B must be singular

B

exactly one of them must be singular

C

both of them are nonsingular

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
If possible assume that A is nonsingular, then `A^(-1)` exists. Thus,
`AB=O implies A^(-1) (AB)=(A^(-1) A)B=O`
`implies IB=O` or `B=O` (contradiction)
Hence, both A and B must be singular.
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