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

  • question_answer
      If A is a square matrix such that \[{{A}^{2}}=A\], then \[{{(I+A)}^{3}}-7A\] is

    A)  3I                   

    B)  0

    C)  I         

    D)  2I

    Correct Answer: C

    Solution :

    [c] Given \[{{A}^{2}}=A.\] Now, \[{{(I+A)}^{3}}-7A={{I}^{3}}+3{{I}^{3}}A+3I{{A}^{2}}+{{A}^{3}}-7A\]\[=I+3A+3A+A-7A\] \[=I+O=I\]


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