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KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    If \[{{A}^{3}}\,=\,O\], \[I\,+\,A\,+\,{{A}^{2}}\]quals

    A) \[I\,-\,A\]

    B) \[{{(\,I\,-\,A\,)}^{-1}}\]      

    C) \[{{(\,I\,+\,A\,)}^{-1}}\]

    D) none of these

    Correct Answer: B

    Solution :

    \[{{A}^{3}}=O\]
    \[(I+A+{{A}^{2}})\,\,(I-A)=I-{{A}^{3}}=I\]
    \[\therefore \]      \[I+A+{{A}^{2}}={{(I-A)}^{-1}}\]
    \[{{A}^{3}}=O\]
    now \[(I+A+{{A}^{2}})\,\,(I-A)=I-{{A}^{3}}=I\]
    \[\therefore \]      \[I+A+{{A}^{2}}={{(I-A)}^{-1}}\]


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