Markov Chains & Long-Run Behavior · Medium problem

A three-state chain has transition matrix $M = \begin{pmatrix} 0.5 & 0.2 & 0.1 \\ 0.3 & 0.6 & 0.3 \\ 0.2 & 0.2 & 0.6 \end{pmatrix}$, where $M_{ij}$ is the probability of moving to state $i$ from state $j$. What is the steady-state probability of state 2? Express your answer as a common fraction.