For any matrix $\textbf{A}$, I know that in the Euclidean L2 induced/operator norm, $\|\textbf{A}\|=\sqrt{\rho(\textbf{A}^{\*}\textbf{A})}$, with \* being the complex conjugate transpose and $\rho$ being the spectral radius. I was told that $\sqrt{\rho(\textbf{A}^{\*}\textbf{A})}=\sqrt{\rho(\textbf{A}\textbf{A}^{\*})}$ because $\textbf{A}\textbf{A}^{\*}$ and $\textbf{A}^{\*}\textbf{A}$ have the same eigenvalues. Why is this true? I can't seem to prove this. Any help would be appreciated. Thank you!