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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

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

    matt grime

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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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