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JEE Main & Advanced Sample Paper JEE Main Sample Paper-11

  • question_answer
    If A and B are two square matrices such that \[B=-{{A}^{-1}}\].then (A + B)2 is equal to

    A)  0                                            

    B)  \[{{A}^{2}}+{{B}^{2}}\]

    C)  \[{{A}^{2}}+2AB+{{B}^{2}}\]      

    D)  \[A+B\]

    Correct Answer: B

    Solution :

     \[{{(A+B)}^{2}}=(A+B).(A+B)={{A}^{2}}+AB+BA+{{B}^{2}}\] ?.1 Since\[B=-{{A}^{-1}}BA\] \[AB=A(-{{A}^{-1}}BA)=-(A{{A}^{-1}})BA[\because A(BC)=(AB)C]\]\[\therefore \]\[AB=-BA\]put in (1), we get \[{{(A+B)}^{2}}={{A}^{2}}-BA+BA+{{B}^{2}}\] \[{{(A+B)}^{2}}={{A}^{2}}+{{B}^{2}}\]


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