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Matrices — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsMatrices1 Mark
MCQ
If A and B are symmetric matrices of same order, $A B-B A$ is a:
  • ✓
    Skew-symmetric matrix
  • B
    Symmetric matrix
  • C
    Zero matrix
  • D
    Identity matrix
✓

Answer

Correct option: A.
Skew-symmetric matrix
(A) Skew-symmetric matrix
Explanation: Given that, $A$ and $B$ are symmetric matrices.
$\Rightarrow \quad A=A^{\prime} \text { and } B=B^{\prime}$
$\begin{array}{ll}\text { Now, } & (A B-B A)^{\prime}=(A B)^{\prime}-(B A)^{\prime}\quad\quad\ldots\text{(i)} \\\Rightarrow & (A B-B A)^{\prime}=B^{\prime} A^{\prime}-A^{\prime} B^{\prime}\quad\text{[By reversal law]}\end{array}$
$\begin{array}{ll}\Rightarrow & (A B-B A)^{\prime}=B A-A B \quad \text { [From Eq. (i)] } \\\Rightarrow & (AB-BA)^{\prime}=-(A B-B A)\end{array}$

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