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

Options

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

Answer

C, D

Explanation

`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.