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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

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

    A)  \[2AB\]                               

    B) \[2BA\]

    C)  \[A\div B\]                        

    D) \[AB\]

    Correct Answer: C

    Solution :

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


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