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J & K CET Engineering J and K - CET Engineering Solved Paper-2011

  • question_answer
    Let A and B both be \[3\times 3\] matrices. Then, \[{{(AB)}^{T}}=BA,\]if

    A)  A is skew-symmetric and B is symmetric

    B)  B is skew-symmetric and A is symmetric

    C)  A and B are skew-symmetric

    D)  None of the above

    Correct Answer: C

    Solution :

    Let A and B are skew-symmetric. \[\Rightarrow \] \[{{A}^{T}}=-A\] and \[{{B}^{T}}=-B\] ?..(i) Given, \[{{(AB)}^{T}}={{B}^{T}}{{A}^{T}}\] \[=(-B)(-A)\] [from Eq. (i)] \[=BA\]


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