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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

  • question_answer
    If A is a \[3\times 3\] non-singular matrix and if \[|A|=3,\]then \[|{{(2A)}^{-1}}|\] is

    A) \[24\]                                   

    B) \[3\]

    C) \[\frac{1}{3}\]                                   

    D) \[\frac{1}{24}\]

    Correct Answer: D

    Solution :

     Given,   \[|A{{|}_{3\times 3}}\ne 0\] and \[|A|=3\] Then,    \[|{{(2A)}^{-1}}|=\left| \frac{1}{2A} \right|=\frac{1}{|2A|}\]                 \[=\frac{1}{{{(2)}^{3}}}.\frac{1}{|A|}\]   \[(\because \,\,|aA|={{a}^{3}}|A|)\]                 \[=\frac{1}{8}.\frac{1}{3}=\frac{1}{24}\]


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