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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If the matrix A is both symmetric and skew symmetric, then:
  • A
    A is a diagonal matrix.
  • ✓
    A is a zero matrix.
  • C
    A is a square matrix.
  • D
    None of these.
✓

Answer

Correct option: B.
A is a zero matrix.
Since, A is symmetric, therefore, A’ = A ...(i)
And A is skew-symmetric, therefore, A’ = –A ⇒ A = –A [From eq. (i)]
⇒ A + A = 0 ⇒ 2A = 0 ⇒ A = 0
Therefore, A is zero matrix.
Therefore, option (B) is correct.

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