Solution
= Solution
Write the <stationary distribution> as a row <vector> $\pi=(a,b,c,d)$. For the first <transition matrix>, $\pi P=\pi$ gives $a=a/2+d$, $b=a/2+b/2$, $c=b/2$ and $d=c$. Hence $b=a$ and $c=d=a/2$. Normalization yields
$$
\boxed{\pi=\left(\frac13,\frac13,\frac16,\frac16\right).}
$$
By the stated common-<stationary distribution> property, this is also the answer for the second <transition matrix>.