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KCET2024MathematicsMatrices

If A is a square matrix, such that A^2=A then (I+A)^3 is equal to

Options

  1. AA-I
  2. B7 A
  3. C7 A+I
  4. DI-7 A

Correct answer

C. 7 A+I

Step-by-step solution

(I+A)^3=I^3+A^3+3 I^2 A+3 A^2 I=I+A^3+3 A+3 A^2=I+A^2 A+3 A+3 A [ A^2=A ]=I+A A+6 A=I+A^2+6 A=I+A+6 A [ A^2=A ]=I+7 A

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