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Nilpotent matirx

  1. Mar 29, 2008 #1
    1. 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?

    2. cant seem to figure out how to get the answer to this one, drawn a mental blank any help would be appreciated
  2. jcsd
  3. Mar 29, 2008 #2
    so B^k = 0 for some k

    say B^2 = 0,

    Notice (I-B)(I + B) = I

    Now what if B^3 = 0

    then (I-B)*something = I

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