What is an example of a Markov Chain with two stationary measures?

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I am trying to come up with a transition matrix for a Markov Chain with two stationary measures, but am not able to construct it. Would anyone have an example? Thanks.

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The two state Markov chain with transition probability matrix $$P = \begin{bmatrix} 1-\alpha & \alpha\\ \beta & 1-\beta \end{bmatrix}$$

can be shown to have an invariant/stationary measure.