Let U be a square matrix such that U^(TT)U = I. Show that det(U) = ±1. How does an intermediate achieve the desired result?

A. det(U^(TT)U) = det(I)
B. U^(TT) = U^(-1)
C. U^(TT)U = UU^(-1)
D. det(U^(TT)) = det(U)
Note: I have removed unnecessary spaces and words to make the question more concise.