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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 24

  • question_answer
    Let A be a square matrix of order 3 such that det. \[(A)=\frac{1}{2}\]. Then det.(adj.\[{{A}^{-1}}\]) is equal to

    A) \[2\]                       

    B)        \[4\]        

    C) \[8\]                      

    D)        \[16\]

    Correct Answer: B

    Solution :

       [b] We know that \[|adj.\,\,A|\,\,=\,\,|A{{|}^{n-1}},\] where n is order of square matrix A. For \[n=3;\] \[|adj.\,{{A}^{-1}}|\,\,=\,\,|{{A}^{-1}}{{|}^{2}}=\frac{1}{|A{{|}^{2}}}=\frac{1}{{{\left( \frac{1}{2} \right)}^{2}}}=4\]           


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