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

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

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

Square matrices of the same order

Square matrices of different order

Rectangular matrices of same order

Rectangular matrices of different order

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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 × n and

B of order p × q, it requires that

n = p ...... (1)

m = p ....... (2)

n = q ...... (3)

form (1) and (3)

p = q ....... (4)

from (1) and (2)

n = m ....... (5)

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

A and B are square matrices and their orders

are one and same .

∴ The addition and multiplication of two matrices

should be of same order and they should be

square matrices.

∴ so, the answer is A. square matrices of the same

order.

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