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If A and B are two matrices such that th...

If A and B are two matrices such that their product AB is
a null matrix, then

A

det `A ne 0 rArr B` must be a null matrix

B

det `B ne 0 rArr A ` must be a null matrix

C

alteast one of the two matrices must be singular

D

if neither det A nor det B is zero, then the given statement
is not possible

Text Solution

Verified by Experts

The correct Answer is:
C, D
`because AB = 0 `
` rArr abs(AB) = 0 rArr abs(A) abs(B) = 0`
or (det A) (det B) = 0
rArr Either det ` A = 0 or det B - 0`
Hence, atleast one of the two matrices must be singular
otherwise this statement is not possible.
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