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

  • question_answer
    Let A and B be \[3\times 3\] matrices of real numbers, where A is symmetric, B is skew symmetric, and \[(A+B)(A-B)=(A-B)(A+B).\] If \[{{(AB)}^{t}}={{(-1)}^{k}}AB\]where \[{{(AB)}^{t}}\] is the transpose of the matrix AB, then k is

    A) Any integer

    B) Odd integer

    C) Even integer

    D) Cannot say anything

    Correct Answer: B

    Solution :

    [b] \[(A+B)(A-B)=(A-B)(A+B)\] \[\Rightarrow AB=BA\] as A us symmetric and B is skew-symmetric \[{{(AB)}^{t}}=-AB\] \[\Rightarrow k\] is an odd integer.


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