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J & K CET Engineering J and K - CET Engineering Solved Paper-2010

  • question_answer
    If A and Bare square matrices of order 3 such that  \[det\text{ }A=1\]  and   \[det\text{ }B=-1~\]then \[det\text{ (-10}\,\text{AB)}\] is equal to

    A)  \[10\]            

    B)  \[-10\]

    C)  \[-1000\]         

    D)  \[1000\]

    Correct Answer: D

    Solution :

    \[\det \,\,A=1,\]  \[\det \,\,B=-1\] \[\det \,(-10AB)={{(-10)}^{3}}\,\det \,(AB)\] \[[\because \,\,\det \,(kA)\,={{k}^{n}}\,\det \,(A)]\] (here, \[n=3\]) \[=-1000\,\det \,(A)\,\det \,(B)\] \[=1+\log \,abc\]


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