# Is spectral radius greater than min row sum for a non-negative matrix?

Suppose a square matrix $A$ has non-negative entries and each row sum is at least $a$. Does it mean that the spectral radius of $A$ is at least $a$?

If $A$ has all positive entries or is irreducible in the Perron-Frobenius sense, then this is clearly true. What if it's not?