Question: Let A be a square matrix. Show that if A^2 = 0, then I - A is invertible and (I - A)^-1 = I +

Let A be a square matrix.

Show that if A^2 = 0, then I - A is invertible and (I - A)^-1 = I + A.

Show that if A^3 = 0, then I - A is invertible and (I - A)^-1 = I +A+A2.

If A^n = 0 for some n 4, is I - A invertible?

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