struggling with the following question, thinking about using hermitian matrix properties, but get lost on the way...
Given the following matrix:
$A = \begin{pmatrix} -2 & 5 & 5\\ 5 & -2 & 5\\ 5& 5 & -2 \end{pmatrix}$
For every complex and not real number $z$: $A - zI $ is invertible.