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

P=

1 0 0 .1 .6 .3 .2 .2 .6

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=

Identity matrix 0 R Q

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

Limiting matrix of P =

Identity matrix 0 FR 0

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

minus

1 0 0 1

is

.6 .3 .2 .6

.4 -.3 -.2 .4

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

.4 -.3 -.2 .4

4 3 2 4

Now, FR is equal to

multiplied by

4 3 2 4

The product is

.1 .2

1 1

This makes the limiting matrix seem like

1 0 0 1 0 0 1 0 0

This matrix just seems strange O_o.