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Homework Help: 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


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    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


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    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.
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