$\rho(A) \geq 0$ for all matrices

$\rho(A^T) = \rho(A)$ (spectral radius is preserved under transpose)

$\rho(A^k) = [\rho(A)]^k$ for positive integers $k$

$\rho(cA) = c \cdot \rho(A)$ for any scalar $c > 0$