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JEE Main & Advanced Sample Paper JEE Main Sample Paper-23

  • question_answer
    Let A and B are two square matrices of order 3 each that det. \[(A)=3\] and det. \[(B)=2\], then the  value or det \[\left( {{\left( adj.\left( {{B}^{-1}}{{A}^{-1}} \right) \right)}^{-1}} \right)\]is equal to  [Note: adj M denotes the adjoint of a square matrix M.]

    A)  6                                

    B)  9

    C)  18                               

    D)  36

    Correct Answer: D

    Solution :

    \[|{{(adj.P)}^{-1}}=\frac{1}{|adj.P|}\,=\frac{1}{|adj.({{B}^{-1}}\,{{A}^{-1}})|}\,=\frac{1}{|{{B}^{-1}}{{A}^{-1}}{{|}^{2}}}\] \[=|{{A}^{2}}|\,\,|{{B}^{2}}|\,={{(3)}^{2}}\,\times {{(2)}^{2}}=9\times 4=36\]


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