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KVPY Sample Paper KVPY Stream-SX Model Paper-19

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

    A) \[\left| \,A\, \right|+K\]

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

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

    D) none of these

    Correct Answer: C

    Solution :

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


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