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Inverse of a Matrix

  1. May 26, 2009 #1
    1 1 1
    1 1 0
    1 0 0

    Find the inverse of this matrix Mod 2

    For the standard inverse I got

    0 0 1
    0 1 -1
    1 -1 0

    Now do I change all those -1's to 1? Or should I have done that at each step and not leave it to the last?

    Is finding the inverse mod n, the same as saying find the inverse over the field k, where k = Fn, where all values correspond to an integer in {0,1,2,..,n-1}? i.e in F3, {0,1,2} the number -1 would correspond to 2.
     
  2. jcsd
  3. May 26, 2009 #2

    Mark44

    Staff: Mentor

    If you change the -1's in the second matrix to 1's, and then multiply by the first matrix, you get I3. For your first question, I don't believe it makes a difference when you change, at intermediate steps or the end.
     
  4. May 27, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What is -1? That is, what is the additive inverse of 1 (mod 2)? That is Mark44's point.
     
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