Q118 / 160 · WBJEE 2009 · Mathematics

If $A$ is a square matrix then,

  • Correct answer
    A
    $\mathrm{A}+\mathrm{A}^{\mathrm{T}}$ is symmetric
  • B
    $\mathrm{AA}^{\mathrm{T}}$ is skew - symmetric
  • C
    $\mathrm{A}^{\mathrm{T}}+\mathrm{A}$ is skew-symmetric
  • D
    $\quad \mathrm{A}^{\mathrm{T}} \mathrm{A}$ is skew symmetric

Solution

Hints: $\left(\mathrm{A}+\mathrm{A}^{\mathrm{T}}\right)^{\mathrm{T}}=\mathrm{A}^{\mathrm{T}}+\left(\mathrm{A}^{\mathrm{T}}\right)^{\mathrm{T}}=\mathrm{A}^{\mathrm{T}}+\mathrm{A}=\mathrm{A}+\mathrm{A}^{\mathrm{T}}$

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

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