1. Not finding help here? Sign up for a free 30min 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!

Commutator of two element in GL(2,5)

  1. Dec 20, 2013 #1
    1. The problem statement, all variables and given/known data

    This is more about checking a solution I've been given is correct, because either my professor is consistently getting this wrong or I am.


    3. The attempt at a solution

    My professor's answers say

    [itex][ \left( \begin{array}{ccc}
    1 & 0 \\
    0 & 4 \end{array} \right),

    \left( \begin{array}{ccc}
    1 & 4 \\
    0 & 1 \end{array} \right)] =

    \left( \begin{array}{ccc}
    4 & 1 \\
    0 & 4 \end{array} \right)[/itex]

    But I get the answer

    [itex]\left( \begin{array}{ccc}
    1 & 3 \\
    0 & 1 \end{array} \right)[/itex]

    I won't go in to explicit detail unless someone asks because I can't be bothered to do the latex, but can anyone confirm which answer is right? My professor does a lot of these through the solutions and I seem to be getting contradictory answers in each case.
     
  2. jcsd
  3. Dec 20, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Assuming GL(2,5) means invertible 2x2 matrices mod 5 and commutator means [A,B]=AB-BA, I don't get either answer. You don't have to TeX, just explain what you mean.
     
  4. Dec 20, 2013 #3
    Apologies, the the commutator of two elements x and y in a group is denoted [x,y], meaning

    [itex] [x,y] = x^{-1}y^{-1}xy [/itex]

    But everything else you said was correct, this is the group of invertible 2x2 matrices mod 5.
     
  5. Dec 20, 2013 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Ah, ok. That makes more sense. If it's the group commutator not the matrix commutator, then I agree with your answer.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted