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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        If A is a skew-symmetric matrix and n is odd positive integer, then\[{{A}^{n}}\]is

    A)  a skew-symmetric matrix

    B)  a symmetric matrix

    C)  a diagonal matrix

    D)  None of the above

    Correct Answer: A

    Solution :

                    Given A is skew-symmetric matrix. \[\therefore \]  \[{{A}^{T}}=-A\] \[\Rightarrow \]               \[{{A}^{n}}={{(-{{A}^{T}})}^{n}}=-{{({{A}^{T}})}^{n}}={{(-{{A}^{n}})}^{T}}\] Hence,\[{{A}^{n}}\]is skew-symmetric matrix.


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