if A is an m x m matrix satisfying A4 0 then IA1SolutionCon

if A is an m x m matrix satisfying A^4 = 0, then (I-A)^-1=

Solution

Consider (I-A) (I +A +A²+A³ ) = I +A +A²+A³ -(A +A²+A³+A⁴ ) = I

So the inverse of

(I-A ) is

I +A +A²+A³