If the matrices A=[ai j] and B=[bi j] are of same order, say m × n, satisfy the commutative law, then

Question

If the matrices A=[ai j] and B=[bi j] are of same order, say m × n, satisfy the commutative law, then (A) A+B=B-A (B) A+B=B+A (C) A+B=A-B (D) None of these

Tardigrade Admin · Accepted Answer

Commutative law If A=[ai j], B=[bi j] are matrices of the same order, say m × n, then A+B=B+A. Now, A+B =[ai j]+[bi j]=[ai j+bi j] =[bi j+ai j] (∵ text addition of numbers is commutative ) =([bi j]+[ai j])=B+A

Q. If the matrices $A = [a_{ij}]$ and $B = [b_{ij}]$ are of same order, say $m \times n$ , satisfy the commutative law, then

$A + B = B - A$

$A + B = B + A$

$A + B = A - B$

None of these

Commutative law If $A = [a_{ij}], B = [b_{ij}]$ are matrices of the same order, say $m \times n$ , then $A + B = B + A$ .
Now,
$A + B = [a_{ij}] + [b_{ij}] = [a_{ij} + b_{ij}]$
$= [b_{ij} + a_{ij}]$
$(∵ addition of numbers is commutative)$
$= ([b_{ij}] + [a_{ij}]) = B + A$

Q. If the matrices A=[aij​] and B=[bij​] are of same order, say m×n, satisfy the commutative law, then

A+B=B−A

A+B=B+A

A+B=A−B