(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the determinant of a unitary matrix is +/-1

2. Relevant equations

<Av,Aw>=<v,w>

Det(AB)=Det(A)*Det(B)

3. The attempt at a solution

Alright, I am aware that <Av,Aw>=<v,w> => A(tA)=I and (tA)A=I so Det(A(tA))=Det(I)=1 thus

Det(A)*Det(tA)=1. However, this is where I am stuck, I am aware that in some cases Det(tA)=Det(A), however this is not obvious in this case, as I cannot take tA to be the elementary defintion of switching rows and columns. How can I prove that Det(tA)=Det(A) ONLY from the fact that <Aw,v>=<w,(tA)v>. This inner product can be absolutely any symmetric bilinear form, so do not assume I mean the dot product.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Det(tA) = Det(A)

**Physics Forums | Science Articles, Homework Help, Discussion**