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## Homework Statement

Let

*A*be an

*n x n*matrix. Show that if A

^{2}=0 then

*I - A*is non-singular and

*(I - A)*

^{-1}= I + A## Homework Equations

## 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 I

**show**that for an n x n matrix? Please help me out.