For $A\in \mathcal{M}\_n(\mathbb{C})$, define:

the spectral radius 

$$
\rho(A)=\max\{|\lambda|:\lambda \mbox{ is an eigenvalue of } A\}
$$

and the norm 

$$
\|A\|=\max\_{|x|=1}|A(x)|
$$
where |.| is the Euclidean norm on $\mathbb{C}^n$.

**Problem:** Find all $A\in \mathcal{M}\_n(\mathbb{C})$ such that $\rho(A)=\|A\|$.

Thank you very much!