JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Matrices

  • question_answer
    If A and B are symmetric matrices of the same order and X = AB + BA and Y = AB - BA, then \[{{(XY)}^{T}}\] is equal to

    A) XY

    B) YX

    C) -YX

    D) None of these

    Correct Answer: C

    Solution :

    [c] Given that \[X=AB+BA\] \[\Rightarrow X={{X}^{T}}\] and \[Y=AB-BA\Rightarrow Y=-{{Y}^{T}}\] Now \[{{(XY)}^{T}}={{Y}^{T}}{{X}^{T}}=-YX\]


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