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

  • question_answer
    If A and B are two matrices such that AB = B and BA = A, then \[{{A}^{2}}+{{B}^{2}}\] is equal to

    A) 2AB

    B) 2BA

    C) A+B

    D) AB

    Correct Answer: C

    Solution :

    [c] We have, \[{{A}^{2}}+{{B}^{2}}=AA+BB\] \[=A(BA)+B(AB)\] \[(\therefore AB=B\,\,and\,\,BA+A)\]             \[=(AB)A+(BA)B\]             \[=BA+AB=A+B\,\,\,\,\,\,\,(\therefore \,AB=B\,\,and\,\,BA=A)\]


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