If the product of two non zero square matrices A and B of the same order is a zero matrix then:

Both are singular

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Atleast one of A or B is singular

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A is non-singular, but B is singular

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A is singular but B is non-singular

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Solution

The correct option is D Atleast one of A or B is singular
we have
$d e t (A B) = d e t (A) d e t (B)$
given $A B = 0$
therefore,
$d e t (A) d e t (B) = 0$
implies atleast one of A&B is singular

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Similar questions

If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
(a) null matrix
(b) singular matrix
(c) unit-matrix
(d) non-singular matrix

Q. If A and B are non-singular matrices of the same order, write whether AB is singular or non-singular.

Q. If A and B are two non-zero square matrices of the same order then AB = O implies that both A and B must be singular.

Two

n \times n

square matrices

A

and

B

are said to be similar if there exists a non-singular matrix

P

such that

P^{- 1} A P = B

A

and

B

are two non-singular matrices, then

Q. Let

A

and

B

be two square matrices satisfying

A B - B A = A

. Then which of the following is (are) TRUE?

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If the product of two non zero square matrices A and B of the same order is a zero matrix then:

The correct option is D Atleast one of A or B is singularwe havedet(AB)=det(A)det(B)given AB=0therefore,det(A)det(B)=0implies atleast one of A&B is singular

The correct option is D Atleast one of A or B is singular
we have
$d e t (A B) = d e t (A) d e t (B)$
given $A B = 0$
therefore,
$d e t (A) d e t (B) = 0$
implies atleast one of A&B is singular