[math] \newcommand{\mathds}{\mathbb}[/math]

Given an Hadamard matrix [math]H\in M_5(\mathbb T)[/math], chosen dephased,

[[math]] H=\begin{pmatrix} 1&1&1&1&1\\ 1&a&x&*&*\\ 1&y&b&*&*\\ 1&*&*&*&*\\ 1&*&*&*&* \end{pmatrix} [[/math]]

prove that the numbers [math]a,b,x,y[/math] must satisfy the following equation:

[[math]] (x-y)(x-ab)(y-ab)=0 [[/math]]