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?