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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 9

  • question_answer
    If A and B are square matrices of the same order such that \[|A|\,=\,|B|=1\] and \[A(adj\,\,A+adj\,\,B)=B,\] then the value of \[|A+B|\] is

    A) 0                       

    B) 1             

    C) 4                     

    D) None of these

    Correct Answer: B

    Solution :

    [b] We have \[|A|\,\,=\,\,|B|=1\] and \[A.(adj\,A+adj\,B)=B\] \[\Rightarrow \,\,\,\,|A|.I+A.adj\,\,B=B\] \[\Rightarrow \,\,\,\,(I+A.adj\,\,B).B={{B}^{2}}\] \[\Rightarrow \,\,\,\,B+A.|B|.I={{B}^{2}}\] \[\Rightarrow \,\,\,\,A+B={{B}^{2}}\] \[\therefore \,\,\,\,\,\,|A+B|\,\,=\,\,|{{B}^{2}}|\,\,=\,\,|B|.|B|=1\]      


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