Obtaining a two step transition matrix in a stationary Markov chain I'm reading the chapter on Markov processes in DeGroot and do not find the explanation for the following thing:
A transition matrix P is specified in the following way:
$$P = \begin{pmatrix}
0.1 & 0.4 & 0.2 & 0.1 & 0.1 & 0.1\\
0.2 & 0.3 & 0.2 & 0.1 & 0.1 & 0.1\\
0.1 & 0.2 & 0.3 & 0.2 & 0.1 & 0.1\\
0.1 & 0.1 & 0.2 & 0.3 & 0.2 & 0.1\\
0.1 & 0.1 & 0.1 & 0.2 & 0.3 & 0.2\\
0.1 & 0.1 & 0.1 & 0.1 & 0.4 & 0.2
 \end{pmatrix}$$
And mentions that to obtain a two step matrix you simply multiply the matrix by itself to obtain $P^2$.
I don't understand how these values are obtained for $P^2$:
$$P = \begin{pmatrix}
0.14 & 0.23 & 0.20 & 0.15 & 0.16 & 0.12\\
0.13 & 0.24 & 0.20 & 0.15 & 0.16 & 0.12\\
0.12 & 0.20 & 0.21 & 0.18 & 0.17 & 0.12\\
0.11 & 0.17 & 0.19 & 0.20 & 0.20 & 0.13\\
0.11 & 0.16 & 0.16 & 0.18 & 0.24 & 0.15\\
0.11 & 0.16 & 0.15 & 0.17 & 0.25 & 0.16
 \end{pmatrix}$$
What am I missing? Should the values simply be multiplied by themselves?

If I understand the question correctly, what you're looking for is matrix multiplication.
