Stationary distribution of identity matrix

Question

I am studying for quiz. I want to find stationary vector for $$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$

I drew the markov picture and tried $x = xP$ but did not get a solution. Does it mean that the stationary distribution does not exist?

Answer 1

Any vector $x$ satisfies the condition

$$ x = x P $$

where $P$ is the identity matrix. The other conditions you need for $x$ to be a stationary distribution are

• It must have non-negative entries
• The sum of its components must be $1$