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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Mock Test - Matrices

  • question_answer
    If \[{{A}^{3}}=0\], then I=A+\[{{A}^{2}}\]equals

    A) \[I-A\]  

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

    C) \[{{(I-A)}^{-1}}\]       

    D) none of these

    Correct Answer: C

    Solution :

    [c] Given \[{{A}^{3}}=0\] Now, \[(I-A)(I+A+{{A}^{2}})\] \[={{I}^{2}}+IA+I{{A}^{2}}-AI-{{A}^{2}}-{{A}^{3}}\] \[=I-{{A}^{3}}=I\] \[\Rightarrow {{(I-A)}^{-1}}=I+A+{{A}^{2}}\]


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