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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If a matrix $A$ is both symmetric and skewsymmetric, then
  • A
    $A$ is a diagonal matrix
  • ✓
    $A$ is a zero matrix
  • C
    $A$ is a scalar matrix
  • D
    $A$ is a square matrix
✓

Answer

Correct option: B.
$A$ is a zero matrix
(b) : $A$ is a symmetric matrix
$
\therefore \quad A^T=A
$
$A$ is also a skew-symmetric matrix
$
\therefore \quad A^T=-A
$
From (i) and (ii), we get
$
A=-A \Rightarrow A=O
$
Hence, $A$ is zero matrix.

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