Expected revisits of the start state

HardExpected Value Stochastic Processes~6m

A symmetric $\pm 1$ walk on $\{0,1,2,3,4\}$ has $0$ and $4$ absorbing and starts at $2$ . What is the expected number of times it is at state $2$ before absorption (counting the start)?

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Expected visits before absorption are the entries of $N=(I-Q)^{-1}$ over the transient states $\{1,2,3\}$ .
You need the start-to-start entry $N_{22}$ ; invert the $3\times3$ matrix.

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Expected revisits of the start state

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