Determinant of the conjugate matrix: Prove that |detA|=1 if A is unitary matrix.

brigitte

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Mar 17, 2018
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I'm proving that |detA|=1 if A is unitary matrix. I got to the point where det(A*)det(A)=1. I know that det(A*)=det(A) conjugated (because determinant is polynomial with real coefficients), but I don't know how to precisely say that. Is there a simple way to prove that?
 
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