signs of the eigenvalues of a Markov matrix

Question

A Markov matrix is a square matrix with nonnegative entries whose row sums are all $1$. From its Wikipedia page, I learn that all the eigenvalues of a Markov matrix are bounded by $1$. But it seems that some of eigenvalues could be complex or negative.

1. Under what condition does a Markov matrix have all real eigenvalues?
2. Under what condition does a Markov matrix have all positive eigenvalues?
3. 2. Under what condition does a Markov matrix have all nonnegative eigenvalues?