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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A$ is a square matrix, then $A-A^{\prime}$ is a
  • A
    diagonal matrix
  • ✓
    skew-symmetric matrix
  • C
    symmetric matrix
  • D
    none of these
✓

Answer

Correct option: B.
skew-symmetric matrix
(b) : As $\left(A-A^{\prime}\right)^{\prime}=A^{\prime}-\left(A^{\prime}\right)^{\prime}=A^{\prime}-A=-\left(A-A^{\prime}\right)$, therefore, $A-A^{\prime}$ is a skew-symmetric matrix.

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