Question

let U be a square matrix such that U transpose*U = I. show that |det U| =1

Answer 1

\[1=Det(I)=Det(U^'U)=Det(U')Det(U)=Det(U)Det(U)=Det(U)^2\]

\[Det(U)=\pm\sqrt{1}=\pm 1\]

thus

\[|Det(U)|=1\]

Answer 2

thanks