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Matrix Determinant

  1. Oct 19, 2009 #1
    Let A, B and C be 3x3 invertible matrices where det(A)=4 , det(B)=4 and det(C) is some non-zero scalar.

    a) det [(C^T)(A^-1)(B^2)(C^-1)]

    b) det [-2(A^2)^T(C^2)(B^-1)(C^-1)^2]


    a)
    What I got is:

    det [(A^-1)(B^2)(C^T)(C^-1)]

    = det [(A^-1)(B^2)(C)(C^-1)]

    = det [(A^-1)(B^2)]

    = [1/det(A)]*[det(B)]^2

    = (1/4)*(4)^2

    = 16/4

    = 4


    b)
    What I got is:

    det [-2(A^2)^T(B^-1)(C^2)(C^-1)^2]

    = (-2)^3 det [(A^2)^T(B^-1)(C^2)(C^-2)]

    = -8 det [(A^2)(B^-1)]

    = -8 [det(A)]^2*[1/det(B)]

    = -8 (4)^2*(1/4)

    = -8 (16)*(1/4)

    = -8*4

    = -32


    Can anyone please tell me, am I getting the right answers for a) and b)?
     
  2. jcsd
  3. Oct 19, 2009 #2

    rock.freak667

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    Homework Helper

    They look correct to me
     
  4. Oct 20, 2009 #3

    tiny-tim

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    Science Advisor
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    Me too. :smile:

    … what's worrying you about them?​
     
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