Question

If $A$ and $B$ are two matrices of same order, then $A+B$ is equal to

• A. $B+A$
• B. $BA$
• C. $(A+B)T$
• D. $A-B$

Answer 1

Answer: (A)

$B+A$

Yes, matrices are commutative.

We can see it as follows:

Let element of $A$ matrix be denoted by a${}_{ij}$ and $B$ matrix be denoted by b${}_{ij}$. Then corresponding elements of $A+B$ matrix will be (a${}_{ij}$ + b${}_{ij}$) and corresponding elements of $B+A$ matrix will be (b${}_{ij}$ + a${}_{ij}$). But since addition is commutative, corresponding elements of $(A+B)$ and $(B+A)$ matrices are the same and hence, both the matrices, $A+B$ and $B+A$ are equal.