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Homework Help: Help with Determinants

  1. Oct 22, 2007 #1
    1. The proof that det(kA) = k^ndetA where A is nxn
    I read somewhere that det(rI(n)) = r^(n)
    so det(rA) = det(rI(n).A) = r^ndetA but I am really confused about how they got that? Is I the identity matrix? What would the det(I) be?
     
  2. jcsd
  3. Oct 22, 2007 #2

    JasonRox

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    Homework Helper
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    You pretty much got it.

    We know that det(AB) = det(A)det(B).

    Therefore,

    det(rA) = det(rI[n]A) = det(rI[n])det(A) = r^n det(I[n]) det(A) = r^n (1) det(A) = r^n det(A)

    I showed every step possible basically.

    Yes, the determinant of I[n] is always 1. It is the identity matrix.
     
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