My attempts: The transition matrix of the corresponding embedded Markov chain is $$T=\begin{pmatrix} 0 & \dfrac{c}{c+d}& \dfrac{e}{e+f}\\ \dfrac{a}{a+b}&0 & \dfrac{f}{e+f}\\ \dfrac{b}{a+b}& \dfrac{d}{c+d} &0 \end{pmatrix}$$ Are the states recurrent or transient?
Method 1: using Corollary 2:
From the directed graph for Exercise 2, there is a single communication class $\{1,2,3\}$ so that the Markov chain is irreducible. Also, the chain is finite, then the chain is recurrent.
Please correct me if I am wrong. Besides, I would like to use the corollary 1.
A state $i$ in a CTMC $\{X(t)\}, t\geq 0$, is recurrent (transient) iff $\sum_{n=0}^{\infty}t^{(n)}_{ii}=\infty (<\infty)$