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Let A be a square matrix satisfying two ...

Let A be a square matrix satisfying two conditions (i) `A^k =0, k in N` (ii) If `A^l = 0` for some `l in N`, then `I >= k`. Prove that `(I - A)` is invertible and its inverse is given by `B=I+A+A^2 +......+ A^(k-1)`

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