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J & K CET Engineering J and K - CET Engineering Solved Paper-2010

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

    A)  \[AB\]           

    B)  \[A+B\]

    C)  \[BA+B\]         

    D)  \[AB+A\]

    Correct Answer: B

    Solution :

    Given,  \[AB=A,\,BA=B\] \[{{A}^{2}}+{{B}^{2}}=AA+BB\] \[=(AB)A+(BA)\,B\] \[=A(BA)+B(AB)=AB+BA\] \[=A+B\]


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