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: Invertible square matrix

  1. Feb 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that the square matrix [tex]2N - I[/tex] is its own inverse if [tex]N^{2} = N[/tex]

    2. Relevant equations
    properties of invertible matrix


    3. The attempt at a solution
    I really don't know where to start here. I know that [tex](2N-I)(2N-I) = I[/tex], but where do I go on from there?
     
  2. jcsd
  3. Feb 28, 2010 #2
    You are correct in calculating (2N-I)(2N-I) and using N2=N in your calculations. If (2N-I)(2N-I)=I, then the desired result is achieved, as this implies [(2N-I)]-1=(2N-I).
     
  4. Feb 28, 2010 #3
    So the answer is simply [tex](2N-I)(2N-I) = I[/tex]? But how did I use [tex]N^{2} = N[/tex]?
     
  5. Feb 28, 2010 #4
    I just assumed you did :)
    The result (2N-I)(2N-I)=I is the desired result. So take (2N-I)(2N-I) and expand it. After you are done that, use N2=N.
     
  6. Feb 28, 2010 #5
    ok, so I get:

    [tex]2N^{2} - 2NI - 2NI + I^{2} = I[/tex]

    [tex]2N - 2N - 2N + I = I[/tex]

    But this doesn't work out.
     
  7. Feb 28, 2010 #6
    The coefficient on N2 is incorrect. It is not a 2.
     
  8. Feb 28, 2010 #7
    Ok I got it. Thanks for the help.
     
  9. Feb 28, 2010 #8
    Cheers.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook