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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    If A is a \[3\times 3\] non-singular matrix, then \[\det \,\,({{A}^{-1}}\,adj\,A)\] is equal to

    A)  \[det\text{ }A\]        

    B)  \[1\]

    C)  \[{{(det\text{ }A)}^{2}}\]      

    D)  \[{{(det\text{ }A)}^{-1}}\]

    Correct Answer: A

    Solution :

    det \[({{A}^{-1}}\,adj\,\,A)\] =det  \[({{A}^{-1}})\,\det \,(adj\,A)\] \[={{(\det \,A)}^{-1}}\,\,{{(\det \,\,A)}^{3-1}}\] \[=\det \,A\]


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