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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    Let A be a matrix of order \[3\times 3\] such that\[|A|=1.\]Let \[B=2{{A}^{-1}}\]and\[C=\frac{adj.A}{2}.\] Then the value of \[|A{{B}^{2}}{{C}^{3}}|,\]is (where |A| represent det. A)

    A)  0                                            

    B) \[\frac{1}{8}\]

    C)  8                                            

    D)  64

    Correct Answer: B

    Solution :

    \[|B|=|2{{A}^{-1}}|={{2}^{3}}|{{A}^{-1}}|=\frac{{{2}^{3}}}{|A|}\] \[|C|=\left| \frac{adj.A}{2} \right|=\frac{1}{{{2}^{3}}}|adj.A|=\frac{|A{{|}^{2}}}{{{2}^{3}}}\] \[|A{{B}^{2}}{{C}^{3}}|=||A|\,|{{B}^{2}}|\,|{{C}^{3}}|\] \[=1\cdot \frac{{{2}^{6}}}{|A{{|}^{2}}}\cdot \frac{|A{{|}^{6}}}{{{2}^{9}}}=\frac{1}{8}\]


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