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Find the inverse of AB:

  1. Mar 9, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the inverse of AB if A^(-1)= [4,0;-2,2] and B^(-1)=[-2,0;-2,3]. (See below for picture/additional information.)


    2. Relevant equations

    Inverse of AB = inverse of A*inverse of B

    3. The attempt at a solution

    Using above equation:

    (AB)^(-1) = [4,0;-2,2]*[-2,0;-2,3] = [-8,0;0,6]

    I don't understand why this is wrong. I calculated it by hand, and then used two different online matrix calculators when I was told it was wrong. The calculators agree with me. Am I entering it incorrectly? Here is a picture of the "full" question: http://imgur.com/foTsK2e.
    Thanks.
     
    Last edited: Mar 9, 2013
  2. jcsd
  3. Mar 9, 2013 #2
    Inverse of AB = inverse of B*inverse of A
    Matrix multiplication does not commute!
     
  4. Mar 9, 2013 #3
    Um, what does commute mean in this context?

    EDIT: Looked it up, and I don't understand why you say that. So what if BA doesn't work (haven't even tested it - don't see how it is applicable).
     
    Last edited: Mar 9, 2013
  5. Mar 9, 2013 #4

    rcgldr

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    If you do the math to find A and B:

    A = (A-1) -1

    B = (B-1) -1

    then multiply A and B, then take the inverse

    (AB)-1

    You'll find it's the same as (B-1) (A-1) and not the other way around. This is because matrix multiplicaion is associative, but not commutative (the next post has a link showing the math).
     
    Last edited: Mar 9, 2013
  6. Mar 9, 2013 #5

    SteamKing

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    Staff Emeritus
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  7. Mar 10, 2013 #6
    So the inverse of AB should be B^(-1)*A^(-1)? Tried it: got the question right.

    Thank you.

    EDIT: My textbook got it right, I just didn't pay attention. Whoops...
     
    Last edited: Mar 10, 2013
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