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KVPY Sample Paper KVPY Stream-SX Model Paper-8

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

    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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