Matrices problem

  • #1
1. A square matrix A is called nilpotent if a^k = 0 for some k > 0. Prove that if A is nilpotent, then I + A is invertible.

2. Show that the equation AB - BA = I has no solutions in n x n matrices with real entries.
 

Answers and Replies

  • #2
radou
Homework Helper
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Regarding 2, try to use the matrix trace function.
 
  • #3
matt grime
Science Advisor
Homework Helper
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1) Forget matrices. You want to find

(1+x)^{-1}

well, what is that as a power series?
 

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