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If A is a nilpotent matrix of index 2 , then for any positive integer n, A(I+A)^n is equal to

Options

  1. AA⁻¹
  2. BA
  3. CA^n
  4. DI_n

Correct answer

B. A

Step-by-step solution

aligned & A^2=0, A^3=A^4= =A^n=0 & then A(I A)^n=A(I+n A) & =A n A^2=A . aligned

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