You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Definition of a Determinant

If A and ...

Question

If $A$ and $B$ are two matrices such that $A B = 0$ and $A$ is non-singular, then

B = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

is singular

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

is non-singular

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B = A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $B$ is singular
$A B = 0$
Therefore
$det (A B) = 0$
$| A B | = 0$
$| A | . | B | = 0$
Now $| A | \neq 0$
Hence $| B | = 0$ .
Therefore, $B$ is singular.

Suggest Corrections

Similar questions

Q. If

A

and

B

are any two matrices such that

A B = 0

and

A

is non-singular, then

A

and

B

are two non-singular square matrices each of

3 \times 3

such that

A B = A

and

B A = B

and

| A + B | \neq 0

, then

| A + B |

is -

Q. If A, B are two n × n non-singular matrices, then
(a) AB is non-singular
(b) AB is singular
(c)

{(A B)}^{- 1} A^{- 1} B^{- 1}

(d) (AB)⁻¹ does not exist

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

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

Join BYJU'S Learning Program

If A and B are two matrices such that AB=0 and A is non-singular, then

The correct option is B B is singularAB=0Thereforedet(AB)=0|AB|=0|A|.|B|=0Now |A|≠0Hence |B|=0. Therefore, B is singular.

If $A$ and $B$ are two matrices such that $A B = 0$ and $A$ is non-singular, then

The correct option is B $B$ is singular
$A B = 0$
Therefore
$det (A B) = 0$
$| A B | = 0$
$| A | . | B | = 0$
Now $| A | \neq 0$
Hence $| B | = 0$ .
Therefore, $B$ is singular.