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Why isn't this working? a simple inverse of a 2x2 matrix

  1. Oct 3, 2005 #1
    Okay i have a simple problem, and its not working!
    I have the following:
    Find a 2x2 matrix
    A =
    -5 3
    2 -9

    A-1 =
    -3/13 -1/13
    2/39 -5/39

    A*A-1 = I
    1 0
    0 1

    but its saying the inverse i got is wrong! how is this?
    det i got was 1/39
     
  2. jcsd
  3. Oct 3, 2005 #2
    Your determinant is actually 39 (not 1/39). Divide the adjoint matrix by that and you should get your answer (provided you calculated the adjoint correctly).
     
    Last edited: Oct 3, 2005
  4. Oct 3, 2005 #3
    thanks for the responce!! But how did u get a det of -39? if a determinant is defined as
    1/(ad-bc)?
    so if i had
    -5 3
    2 -9

    (-5)(-9) -(3)(2) = 45 - 6 = 39, and its under 1, so 1/39?
    I also tried ur answer, when u say divide the adjoint matrix, do u mean divide the matrix after switching a and d, and negating b and c? I tried that and it was also wrong with ur det
     
  5. Oct 3, 2005 #4
    The determinant of a 2x2 matrix is ad-bc. I meant to say 39, not -39.
     
    Last edited: Oct 3, 2005
  6. Oct 3, 2005 #5

    TD

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    Homework Helper

    No!

    The inverse is 1/det(A) * adj(A) where 1/det(A) = 1/(ad-bc) so det(A) = ad-bc and not 1/(ad-bc).
     
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