1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrices problem

  1. Feb 2, 2007 #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.
     
  2. jcsd
  3. Feb 2, 2007 #2

    radou

    User Avatar
    Homework Helper

    Regarding 2, try to use the matrix trace function.
     
  4. Feb 2, 2007 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    1) Forget matrices. You want to find

    (1+x)^{-1}

    well, what is that as a power series?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?