Sure, here is an example of a Markov chain in matrix form:

[0.6 0.4]
[0.3 0.7]

This is a 2x2 transition matrix, where each entry represents the probability of transitioning from one state to another. For example, the top left entry 0.6 means there is a 0.6 probability of transitioning from state 1 to state 1.

The rules for determining if a transition matrix represents a Markov chain are:

1. All entries are >= 0 (probabilities cannot be negative)
2. Each row sums to 1 (probabilities must sum to 1)
3. The transitions only depend on the current state and not on the previous states (the Markov property)

So in the example matrix I gave, it satisfies rules 1 and 2, and if the transitions only depend on the current state, then it satisfies rule 3 and represents a Markov chain.

In general, if a matrix satisfies rules 1 and 2, and the probabilities of transitioning to a future state only depend on the current state, then it can be classified as a Markov chain transition matrix.
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