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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

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

    A) \[I\]                                      

    B) \[A+B\]

    C) \[2AB\]                                

    D) \[2BA\]

    Correct Answer: B

    Solution :

     Given,                  \[AB=B,BA=A\] Then,    \[{{A}^{2}}+{{B}^{2}}=A.A+B.B\]  \[=A(BA)+B(AB)\]           [From Eq. (i)] \[=(AB)A+(BA)B\]   (by commutative law) \[=BA+AB\]        [From Eq. (i)] \[=A+B\]              [From Eq. (i)]


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