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

Matrices

Solution:

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