Please help me, I don't know where to start.
Consider the matrix:
\begin{bmatrix}a&b&c&d&e\\e&a&b&c&d\\d&e&a&b&c&\\c&d&e&a&b\\b&c&d&e&a\end{bmatrix}
with $a,b,c,d,e \in \mathbb{C}$.
Show that the eigenvalues of this matrix are:
\begin{equation}\lambda_1 = a+b\zeta+c\zeta^2+d\zeta^3+c\zeta^4\\ \lambda_2= a+b\zeta^2+c\zeta^4+d\zeta+e\zeta^3\\ \lambda_3= a+b\zeta^3+c\zeta+d\zeta^4+e\zeta^2\\ \lambda_4=a+b\zeta^4+c\zeta^3+d\zeta^2+e\zeta\\ \lambda_5=a+b+c+d+e\\ \end{equation}
Where $\zeta$ is a fifth primitive root of 1.