Count routes using powers of a connection matrix
A network of teams linked by recorded matches is shown. Each line records one match between the teams
Use the order Orbits, Falcons, Comets for the rows and columns of connection matrix \(C\). Rows name the starting vertex and columns name the ending vertex
\[C = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 2 \\ 1 & 2 & 0 \end{bmatrix}\]