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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer
        If A is a skew symmetric matrix, then the matrix \[{{B}^{T}}AB\]is

    A)  symmetric         

    B)  skew symmetric

    C)  cant say              

    D)  None of these

    Correct Answer: B

    Solution :

                                    Since, A is skew symmetric matrix \[\therefore \]  \[{{A}^{T}}=-A\] Now,\[{{({{B}^{T}}AB)}^{T}}={{B}^{T}}{{A}^{T}}{{({{B}^{T}})}^{T}}\](By reversal law)                 \[={{B}^{T}}{{A}^{T}}B\]                                \[[\because {{({{B}^{T}})}^{T}}=B]\]                 \[={{B}^{T}}(-A)B\]                 \[=-{{B}^{T}}AB\]                             \[(\because {{A}^{T}}=-A)\] Hence,\[{{B}^{T}}AB\]is skew symmetric matrix.


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