Question

If $A$ and $B$ are two matrices such that $AB$ and $A+B$ are both defined then $A$ and $B$ are

• A. Square matrices of the same order
• B. Square matrices of different order
• C. Rectangular matrices of same order
• D. Rectangular matrices of different order

Answer 1

The correct option is A Square matrices of the same order

For the addition of two matrices,it is required that

the matrices should be of the same order.

For multiplication of two matrices A of order $m\times$ n and

B of order $p\times q,$ it requires that

$n=p----\left(1\right)$

$m=p----\left(2\right)$

$n=q----\left(3\right)$

form (1) and (3)

$p=q-------\left(4\right)$

from (1)and (2)

$n=m-----\left(5\right)$

From (4)and (5),we can conclude that

A and B are square matrices and their orders

are one and same .

$\therefore$ The addition and multiplication of two matrices

should be of same order and they should be

square matrices.

$\therefore$ so, the answer is A. square matrices of the same

order.