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This is not a homework exercise, so I decided to post it here. Hopefully one of you could help.

I would like to find an explicit expression for (I-A)^(-1), provided that A is a squared matrix (nxn) and A^k = 0. It is also given that I-A^k = (I-A)(I+A+A^2+...+A^(k-1)).

I understand that by definition the inverse matrix of I-A will be (I+A+A^2+...+A^(k-1)), but is there a way to arrive at a more simplified, explicit expression (yet without knowing what A is)?

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# Explicit expression for inverse of I-A

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