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Simple Matrices proof using Mathematica help

  1. Jan 18, 2013 #1
    Simple Matrices proof using Mathematica help!!!

    1. The problem statement, all variables and given/known data

    Hey guys, I'm trying to prove that

    (AB)-1 = B-1 A-1
    and also the one that looks the same but is with transpose of the matrices

    making A and B arbitrary 3x3 matrices. I made

    A = {{a_1,a_2,a_3}...}
    B = {{b_1,b_2,b_3}...}

    and I was able to prove the Transpose one by typing "Transpose[A B] == Transpose * Transpose[A] " and it spit out the word "True"

    However, when I write "Inverse[A B] == Inverse Inverse[A] ", it does not spit out the word true, rather it spits back out the matrices expanded. Does anyone know how to tweak it so that it'll spit out either the words true or false? Thanks


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 19, 2013 #2

    Simon Bridge

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    Re: Simple Matrices proof using Mathematica help!!!

    ... and checking that the inverse exists?
    check syntax - did you write the above or did you write:

    Inverse[A B] == Inverse*Inverse[A]

    (I can't remember if it matters)

    I find that the inverse function does some rounding off, and the rounding is different if I do inverse[A*B] and when I do inverse[A]*inverse, so whenever I do Inverse[A*B] == Inverse*Inverse[A] it returns "false".
     
    Last edited: Jan 19, 2013
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