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Homework Help: Linear algebra adjoint proof question

  1. Mar 2, 2013 #1
    1. The problem statement, all variables and given/known data

    I dont understand how line five counting from the top in the attached image. How does det (A^-1 det A) become (detA)^n? I get that the A^-1 was factored out but I dont get how (detA )= (detA)^n. Thank you...

    http://img28.imageshack.us/img28/8742/20130302114549.jpg [Broken]

    Uploaded with ImageShack.us
    2. Relevant equations

    Properties of determinates?

    3. The attempt at a solution

    This is the only part of the proof I dont get and i dont know what rule is det A det equal to...

    Attached Files:

    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Mar 2, 2013 #2


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    hi baird.lindsay! :smile:

    (try using the X2 button just above the Reply box :wink:)
    it doesn't, it becomes (detA)n times det(A-1)

    this is because, for any number k and for any matrix M, det (kM) = kndet(M) :wink:

    (and detA is a number)
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