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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Types of matrices, Algebra of matrices

  • question_answer
    If A and B are two matrices such that \[AB=B\]and \[BA=A,\] then \[{{A}^{2}}+{{B}^{2}}=\] [EAMCET 1994]

    A) \[2AB\]

    B) \[2BA\]

    C) \[A+B\]

    D) \[AB\]

    Correct Answer: C

    Solution :

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


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