A Few Matrix Applications

Example:

Suppose we have 3 cities with adjacency matrix:

$A = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix}$

This means:
City 1 → City 2
City 2 → City 3

Compute $A^2$: