How to solve this simple 2D Markov chain

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I have 2D Markov chain like below : enter image description here

I have already solved for $p_{b,0}$ and $p_{0,d}$ like this :

$$p_{b,0} = \rho^bp_{0,0}$$ $$p_{0,d} = \rho^dp_{0,0}$$

But I don't know how to get $p_{b,d}$. So far I know that :

$$\sum\limits_{b=0}^B\sum\limits_{d=0}^Dp_{b,d}=1$$ and

$$p_{b,d} = (something)p_{b,0}$$

Then my final goal is to obtain $p_{0,0}$ formula.

Do you know how to get "something" so I can obtain $p_{b,d}$ here?

Thank you for your help

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