# Matrix Algebra Find an inverse for I-A

Suppose A^n=0 for some n>1. Find an inverse for I-A.

I don't understand how to do this. It isn't homework, but I'm just studying.

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Dick
Homework Helper
If r were a real number with |r|<1 then 1/(1-r)=1+r+r^2+r^3+... It's a geometric series. Substitute r=A and see what you can conclude. Then prove it's true.

HallsofIvy
$$I- A^n= (I- A)(I+ A^2+ A^3+ \cdot\cdot\cdot+ A^{n-1})$$
And, of course, since $A^n= 0$, $I- A^n= ?$