(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

LetAbe ann x nmatrix. Show that if A^{2}=0 thenI - Ais non-singular and(I - A)^{-1}= I + A

2. Relevant equations

3. The attempt at a solution

Ok, so I started off with finding the general form of a 2x2 matrix which when squared gives a zero matrix, and all the properties above are satisfied. But how do Ishowthat for an n x n matrix? Please help me out.

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# Matrices/Linear Algebra Proof

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