finding asyptotic distribution in a markov chain

I have a transition matrix of form

P = [ 0 1 0; 1/2 1/2 0; 0 1/2 1/2]

i find the asymptotic distributin that is [ 1/3 2/3 0] with starting value [ 0 0 1] This we are wanted to show on paper an even in matlab.

our teacher has given us a clue to use,

>> pi = ([P-eye(3))'; [1 1 1]]\ [zeros(3,1);1])'

for my questiong is how do i find the asymptotic distribution and is the given clue correts? can not really trust the teacher since he made several misstakes before