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  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    If A be a square matrix and\[A+{{A}^{T}}\]is a symmetric matrix, then\[A-{{A}^{T}}\]is

    A)  a unit matrix

    B)  a symmetric matrix

    C)  a skew-symmetric matrix

    D)  a zero matrix

    Correct Answer: C

    Solution :

    \[{{(A-{{A}^{T}})}^{T}}={{A}^{T}}-{{({{A}^{T}})}^{T}}={{A}^{T}}-A\] \[[\because {{({{A}^{T}})}^{T}}=A]\] \[=-(A-{{A}^{T}})\] Hence\[A-{{A}^{T}}\]is skew' symmetric matrix.


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