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

Diagonalize explicitely the third flat matrix, namely

[[math]] \mathbb I_3 =\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\end{pmatrix} [[/math]]

and then study as well the general case, that of the matrix [math]\mathbb I_N[/math].