Suppose the answer is Yes. Then suppose we add two more states $i\ne j$ with $P_{i,j}=1$ and $P_{j,i}=1$. In this case $P^n$ does not converge because P_{j,i}=1$, and no other state can go to states$P^n_{i,i}$is 0 i$ or 1 depending on whether $n$ j\$. Then for the new matrix the assumptions are still satisfied, but now the answer is odd or evenNo. Therefore the answer must be No.