Transient state in a Markov chain

Let $\{X_n : n \ge 0\}$ be a homogeneous Markov chain with state space $S = \{1, 2, \dots, 7\}$ and transition probability matrix $P = \begin{pmatrix} \frac13 & 0 & \frac23 & 0 & 0 & 0 & 0 \ 0 & \frac13 & 0 & \frac13 & 0 & \frac13 & 0 \ \frac12 & 0 & \frac12 & 0 & 0 & 0 & 0 \ 0 & \frac12 & 0 & \frac14 & 0 & \frac14 & 0 \ \frac12 & 0 & 0 & 0 & \frac14 & \frac14 & 0 \ 0 & \frac23 & 0 & \frac16 & 0 & \frac16 & 0 \ \frac13 & \frac13 & 0 & 0 & 0 & 0 & \frac13 \end{pmatrix}$. Then which of the following statements is correct?