As the title says I have to answer the following: Identify integers $1 \leq n /leq 20$ where $p_{0,0}^{(n)} > 0$ by using a transition matrix.
I know this is with the states {0,1,2,3,4,5,6,7} and I have drawn my transition diagram. (linked in the comments). However I am unsure about how you go about answering the question.
Any help would be greatly appreciated.