Markov chains/limiting matrix

Hello. Can someone please help in finding the limiting matrix of the following transitional matrix of an absorbing Markov chain:

P=

I have tried finding the limiting matrix myself but my answer does not seem to be right. Can you please check if it's alright?

The matrix P is in standard form, which is the form

P=

And I know that the limiting matrix must be in this form:

Limiting matrix of P =

F is the fundamental matrix for P. It is equal to (I - Q)^-1.

minus

is

to the power of -1 (or in inverse) is

Now, FR is equal to

multiplied by

The product is

This makes the limiting matrix seem like

This matrix just seems strange O_o.

Re: Markov chains/limiting matrix

Re: Markov chains/limiting matrix

Thank you for your help, Soroban! I am relieved that the answer is alright! I cross-checked the answer many times and couldn't find another answer but still felt, for some reason, suspicious of it.