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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 25

  • question_answer
    If A, B and C are \[n\times n\]matrices and det = 2, det(5) = 3 and det = 5, then the value of the det\[({{A}^{2}}B{{C}^{-1}})\]is equal to

    A) \[\frac{6}{5}\]  

    B)        \[\frac{12}{5}\]

    C) \[\frac{18}{5}\]             

    D) \[\frac{24}{5}\]

    Correct Answer: B

    Solution :

    [b]: We have,\[\left| A \right|=2,\left| 5 \right|=3\]and \[\left| C \right|=5\] ...de, \[({{A}^{2}}B{{C}^{-1}})=|{{A}^{2}}B{{C}^{-1}}|=\frac{|A{{|}^{2}}|B|}{|C|}=\frac{4.3}{5}=\frac{12}{5}\]


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