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Algebra help!

  1. Oct 2, 2005 #1
    I am having trouble with particular algebra question. I dont know where to start and it would be greatly appreciated if someone could point me in the right direction.

    Here is the questoin:

    Let V be a vector space, where T is a linear map of V
    prove if T^2 = 0 then I - T is bijective where I is the identity matrix

    I tried (I-T)(I+T) = I - T^2 which equals I, but i am not sure where to go from here or if this even correct.
    thanks for the time and help
  2. jcsd
  3. Oct 2, 2005 #2
  4. Oct 2, 2005 #3
    You are done!
    You just showed that [itex]I-T[/itex] is invertible/bijective by showing that [itex](I-T)(I+T) = (I+T)(I-T) = I[/itex]. Which means, by definition, [itex](I-T)^{-1} = (I+T)[/itex]
  5. Oct 3, 2005 #4
    thx for the help incredible
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