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Linear Algebra Proof involving idempotency

  1. Sep 24, 2014 #1
    1. The problem statement, all variables and given/known data
    I = Identity matrix
    Suppose that A^2 = A. Prove that I - 2A = (I - 2A)^-1


    2. Relevant equations
    ahh don't know what to put here


    3. The attempt at a solution
    So I have to prove this thing is it's own identity... interesting..

    I - 2A = I - 2A^2

    (I - 2A^2)*(I - 2A)^-1 = I

    Distributive law?
    Idk honestly this is all I have gotten.. And it's probably not the right direction, just trying to put all the information I know into one line I guess. Any Mathamavericks out there wanna help a noob out?
     
  2. jcsd
  3. Sep 24, 2014 #2

    Mark44

    Staff: Mentor

    To show that A and B are inverses -- IOW, that B = A-1 -- show that AB = I.
     
  4. Sep 25, 2014 #3
    Isn't that what I set up? I don't know how to solve it
     
  5. Sep 25, 2014 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You want to show (1-2A) is its own inverse. I.e. (1-2A)*(1-2A)=I.
     
  6. Sep 25, 2014 #5

    Mark44

    Staff: Mentor

    What you wrote, Psychonaut, was (1-2A)*(1-2A)-1=I. Do you see the difference?
     
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