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Homework Help: Det(A^n) = det(A)^n

  1. Oct 24, 2007 #1
    Question. Prove det(A^n) = det(A) ^ n

    I have:

    det(AB) = det(A)det(B) (holds for any number of factors)
    set A=B
    det(AA) = det(A)det(A)
    det(A^2) = det(A)^2 ?

    Is this enough for a proof?
  2. jcsd
  3. Oct 24, 2007 #2


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    Homework Helper

    Of course not, since you didn't prove what you need to prove. Hint: induction.
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