First slide

Applications of determinant

Question

Let A and B be two non-null square matrices. If the product AB is a null matrix, then

Moderate

A

A is singular
B

B is singular
C

A is non-singular
D

B is non-singular

Solution

Let B be non-singular, then B^–1 exists.
Now, AB = O (given)
⇒ (AB) B^–1 = OB^–1
(post-multiplying both sides by B^–1)
⇒ A (BB^–1) = O (by associativity)
⇒ AI_n = O ( $∵$ BB–1 = In)
⇒ A = O
But A is a non-null matrix. Hence, B is a singular matrix.
Similarly it can be shown that A is a singular matrix.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App