Matrix Algebra Find an inverse for I-A

[TorinLiRoxMe]

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.

 

[Dick]

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]

Or, essentially the same thing,
$$I- A^n= (I- A)(I+ A^2+ A^3+ \cdot\cdot\cdot+ A^{n-1})$$

And, of course, since $A^n= 0$, $I- A^n= ?$