Q80 / 180 · KCET 2017 · Mathematics

If a matrix \( \mathrm{A} \) is both symmetric and skewsymmetric, then

  • A
    \( A \) is diagonal matrix
  • Correct answer
    B
    \( \mathrm{A} \) is a zero matrix
  • C
    \( \mathrm{A} \) is scalar matrix
  • D
    \( A \) is square matrix

Solution

For symmetric matrix, we know that: $A^{T}=A \rightarrow(1)$ For skew-symmetric matrix, we know that: $A^{T}=-A \rightarrow(2)$ So, $A=-A \Rightarrow A=0$ Therefore, matrix $\mathrm{A}$ is a zero matrix.

Hence, the correct answer is option: 'B'.

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