If A and B are square matrices of equal degree, then which… — JEE Main 1995 Mathematics PYQ

1995

A

and

B

are square matrices of equal degree, then which one is correct among the following?

A.
$A + B = B + A$
B.
$A + B = A - B$
C.
$A - B = B - A$
D.
$AB = BA$

Show answer and solution

Correct option: A

Solution

Matrix addition is commutative: each (i,j) entry of A+B is aᵢⱼ + bᵢⱼ, which equals bᵢⱼ + aᵢⱼ (by commutativity of real numbers), giving B+A. So A+B = B+A always holds for matrices of equal order.

[1995]

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