If A and B are two matrices such that A B is of order n , then which one of the following is correct?

Correct answer: D. Orders of A and B need not be the same. Let A is matrix of order n × a and B is matrix of order b × n . Now, Hence, order of A and B need not to be same.

NDA 2021

Exam: NDA
Year: 2021
Subject: Mathematics
Chapter: Matrices

NDA 2021 · Mathematics · Matrices

If A and B are two matrices such that A B is of order n , then...

A

and

B

are two matrices such that

A B

is of order

n \timesn

, then which one of the following is correct?

Options

A $A$ and $B$ should be square matrices of same order.
BEither $A$ or $B$ should be a square matrix.
CBoth $A$ and $B$ should be of same order.
DOrders of $A$ and $B$ need not be the same.

Correct answer

D. Orders of $A$ and $B$ need not be the same.

Step-by-step solution

Let

A

is matrix of order

n \times a

and

B

is matrix of order

b \times n

. Now,

Hence, order of

A

and

B

need not to be same.

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