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**1. Homework Statement**

If B is any nilpotent matrix, prove that I-B is invertible and find a formula for (I-B)^-1 in terms of powers of B.

**3. The Attempt at a Solution**

If I make a matrix <<ab,cd>> then if 1/(ad-bc)[tex]\neq[/tex]0 then the matrix has an inverse. Since I think all nilpotent matrices have a 0,0,0 leading diagonal with the other diagonal being not fully "0"s. Wouldn't it be impossible for nilpotent matrices to not have an inverse? I think I may have my wording jumbled.