Consider an adjacency matrix A with elements $[A{]}_{ij}=1$ if one can reach state i from state $j$

in one time step, and $0$ otherwise. Show that the matrix $[A^k{]}_{ij}$ represents the number of paths

that lead from state $j$ to $i$ in $k$ time steps. Outline an algorithm that will find the minimum

number of steps to get from state $j$ to state $i.$

Note: you don't need to write code, describe the approach mathematically and verbally.