Consider two colorless balls in a box, in the n-step, i choose a random ball and throw a coin. if the choose ball is colorless and the coin falls head, then i paint red the ball; if the coin falls cross then i paint black the ball and in other case i keep the ball in the box. If the ball is colored, then i change the color of the ball no matter if the coin falls heads or cross. I have to do the transition matrix and i was thinking in $S={0,1,2}$ the state space and 0 means colorless, 1 is the red color and 2 is the black color and i was thinking in the transition matrix like this:
$$ \begin{pmatrix} 0 & 1/2 & 1/2 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ \end{pmatrix} $$ but i do not know if the transition matrix is in coordenates $(x,y)$ where $x$ and $y$ belongs of $S$, because i do not consider the fact of two balls in the box, just i consider the fact when i take the ball and i know the color from this ball.