Steady State

[hifer]

Can anyone tell me when will a transition matrix never reach steady state? In the textbook it says "If T^2 contains any zeros, then it is not possible to reach a steady state"

But I've done a question with a 3x3 transition matrix containing 0 elements and reached steady state, but i'm unable to achieve this using a 2x2 matrix.

Btw, the 3x3 transition matrix i used was:
[ .85  .25  .5 ]
[ .15  .75  .5 ]
[   0    0     0 ]
It does contain 0 elements when T^2 and reaches steady state when T^80

[Mystery]

Can anyone tell me when will a transition matrix never reach steady state? In the textbook it says "If T^2 contains any zeros, then it is not possible to reach a steady state"

But I've done a question with a 3x3 transition matrix containing 0 elements and reached steady state, but i'm unable to achieve this using a 2x2 matrix.

Btw, the 3x3 transition matrix i used was:
[ .85  .25  .5 ]
[ .15  .75  .5 ]
[   0    0     0 ]
It does contain 0 elements when T^2 and reaches steady state when T^80

say the bottom line was location A [0  0  0]

at that location no steady state would be reached, every other element in the matrix will have its own steady state. Hope that clears it up