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KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • question_answer
    If B is adjoint of A which is \[n\times n\] matrix, then \[|AB+K{{I}_{n}}|\,\,=\]

    A) \[|A|+\,\,K\]                 

    B) \[|A|+\,\,{{K}^{n}}\]

    C) \[{{(|A|+\,\,K)}^{n}}\]           

    D) none of these

    Correct Answer: C

    Solution :

    \[\because \]       \[A\,(adj\,A)=\,\,|A|{{I}_{n}}\] \[\because \] \[|AB+K{{I}_{n}}|\,\,=\,\,||A|{{I}_{n}}+K{{I}_{n}}|\,\,=\]\[{{(|A|+K)}^{n}}|{{I}_{n}}|\,\,={{(|A|+K)}^{n}}\] \[\therefore \]      Ans. [c]           


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