1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook