A square matrix A is said to be nilpotent of index m . If A m = 0 , now, if for this A, ( I − A ) n = I + A + A 2 + … + A m − 1 , then n is equal to

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Let B = I + A + A 2 + … + A m − 1 . ⇒ B ( I − A ) ⇒ B ⇒ n ​ = ( I + A + A 2 + … + A m − 1 ) ( I − A ) = I − A m = I = ( I − A ) − 1 = − 1 ​

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