Let $P$ denote the transition matrix and $\pi$ be the vector ($1 \times 8$)of steady-state probabilities. $\pi_1$ is the proportion of time spent in state $1$.
I have $P$, an $8\times 8$ matrix, hence I need to solve $\pi P=\pi$ Additional condition is that $\sum \pi_i =1$
Rearranging $\pi P-\pi=0$ or $\pi(P-I)=(0,...,0)$.
Now $\pi = 0\times (P-I)^{-1}=0$ which is not true.
I don't really want to solve all 8 equations, because that is a lot of hassle. I'm trying to use MATLAB to give me an easy solution.