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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A$ and $B$ are two matrices of same order, then $A + B$ is equal to :
  • ✓
    $B + A$
  • B
    $BA$
  • C
    $(A + B)^T$
  • D
    $A - B$
✓

Answer

Correct option: A.
$B + A$
Yes, matrices are commutative.
We can see it as follows, Let element of $A$ matrix be denoted by $\text{a}_\text{ij}$​ and $B$ matrix be denoted by $\text{b}_\text{ij},$​
Then corresponding elements of $\text{ A + B}$ matrix will be $(\text{a}_\text{ij}​ +\text{b}_\text{ij}​) $ and corresponding
elements of $\text{B + A}$ matrix will be $(\text{b}_\text{ij}​ +\text{ a}_\text{ij}​) $ But since addition is commutative, corresponding elements
of$\text{ A + B}$ and $\text{B + A}$ matrices are the same, So they are equal.

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