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First for all I want to say that I deal with Markov Chains only second day so I have some problems with terminology. Sorry for that.

I need to solve following matrix:

enter image description here

Now in I need to compute FR. In order to compute FR I need to find F first which is (I-Q)^-1.

So my question is what if I and Q have different shape. On the image above Q is smaller than I. And what about case when Q is larger?

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$"I"$ that you see in $(I-Q)^{-1}$is an identity matrix and is of the same dimension as that of Q. The $"I"$ that you see in the image is also an identity matrix by construction and lets you know the number of absorbing states that you have in the system . This one and Q need not have the same dimension.