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KCET2025MathematicsMatrices

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

Options

  1. AI - A
  2. BA - I
  3. CI + A
  4. D- I - A

Correct answer

A. I - A

Step-by-step solution

A ^2= A . aligned & (I-A)^3=(I-A) (I-2 A+A^2 ) & =(I-A)(I-2 A+A) & =(I-A)(I+A) & =I-A^2=I-A aligned

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