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Determinant question

  1. Dec 11, 2007 #1
    Prove if A is orthogonal matrix, then |A|=+-1
    A[tex]^{-1}[/tex]=A[tex]^{T}[/tex]
    AA[tex]^{-1}[/tex]=AA[tex]^{T}[/tex]
    I=AA[tex]^{T}[/tex]
    |I|=|AA[tex]^{T}[/tex]|
    1=|A|*|A[tex]^{T}[/tex]|//getting to the next step is where i get confused. Why is |A|=|A[tex]^{T}[/tex]|
    1=|A|*|A|
    1=|A|[tex]^{2}[/tex]
    +-1=|A|
     
    Last edited: Dec 11, 2007
  2. jcsd
  3. Dec 11, 2007 #2
    I think there is an error in your question. For matrices to be orthogonal A_inverse= A_transpose.

    Sorry I am not yet familiar with LATEX.
     
  4. Dec 11, 2007 #3

    morphism

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    Science Advisor
    Homework Helper

    This is a standard result. You should probably find it in your textbook, or try to prove it yourself.
     
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