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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    Let\[A\]and\[B\]be two symmetric matrices of same order. Then, the matrix\[AB-BA\]is

    A)  a symmetric matrix

    B)  a skew-symmetric matrix

    C)  a null matrix

    D)  the identity matrix

    Correct Answer: B

    Solution :

    Given,   \[A=A,\,\,B=B\] Now,     \[(AB-BA)=(AB)-(BA)\]                 \[=BA-AB\]                 \[=BA-AB\]                 \[=-(AB-BA)\] \[\therefore \]\[AB-BA\]is a skew-symmetric matrix.


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