Let n ≥ 2 be an integer. Let A : Cn → Cn be the linear transformation defined by \(A\left(z_{1}, z_{2}, \ldots, z_{n}\right)=\left(z_{n}, z_{1}, z_{2}, \ldots, z_{n-1}\right)\). Which one of the following statements is true for every n ≥ 2?
1
A is nilpotent.
2
All eigenvalues of A are of modulus 1.
3
Every eigenvalue of A is either 0 or 1.
4
A is singular.