Which of the following statements is/are true for an $N \times N$ unitary matrix $U$ ($U^\dagger U = I$)?
(A)
All eigenvalues of $U$ have absolute value equal to $1$
(B)
The rows and columns of $U$ form orthonormal bases of $\mathbb{C}^N$
(C)
|\det(U)| = 1
(D)
All diagonal elements of $U$ must be strictly real