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Determinant of an orthogonal matrix

  1. Sep 21, 2009 #1
    How is it the determinant of an orthogonal matrix is [tex]\pm1[/tex].
    Is it:
    Suppose Q is an orthogonal matrix [tex]\Rightarrow [/tex] 1 = det(I) = det(QTQ)
    = det(QT)det(Q) = ((det(Q))2
    and if so, what is it for -1.
  2. jcsd
  3. Sep 21, 2009 #2
    Never mind, got it.
  4. Sep 21, 2009 #3
    Maybe you can share your new knowledge with the forum so that when other users see the question they can also see the answer!
  5. Sep 21, 2009 #4
    Suppose Q is orthogonal, then ATA = In
    [tex]\Rightarrow[/tex] det(A)det(ATA) = det(A)det(A) = (det(A))2 = 1
    Which implies that det(A) = [tex]\pm\sqrt{1}[/tex] = [tex]\pm1[/tex]
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