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Question

A square matrix A is said to be nilpotent of index m. If Am=0,now,if for this A ,(IA)n=I+A+A2+...+Am1,then n is equal to
  1. m
  2. - m
  3. - 1
  4. 0


Solution

The correct option is C - 1
Let B=I+A+A2+...+Am1
B(IA)=(I+A+A2+...Am1)(IA)
=IAm=I
B=(IA)1n=1

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