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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

  • question_answer
    Suppose A is a matrix of order 3 and\[B=|A|{{A}^{-1}}.\]If \[|A|=-5,\]then\[|B|\]is equal to:

    A)  1                                            

    B)  \[-5\]

    C)  \[-1\]                   

    D)         \[25\]

    E)  \[-125\]

    Correct Answer: D

    Solution :

    Given A is a matrix of order 3 and \[B=|A|{{A}^{-1}},|A|=-5\] \[\therefore \]  \[B=|A|\frac{(adj\,A)}{|A|}\Rightarrow B(adj\,A)\] \[\Rightarrow \]               \[|B|=|adj\,A|=|A{{|}^{3-1}}\]                                 \[=|A{{|}^{2}}\]                                 \[=25\]


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