Question: 2. Let A be the adjacency matrix for a graph. That is Aij-1 if i, j are adjacent and 0 otherwise. Prove that Ak, is

2. Let A be the adjacency matrix for a graph. That

2. Let A be the adjacency matrix for a graph. That is Aij-1 if i, j are adjacent and 0 otherwise. Prove that Ak, is the number of paths of length k starting at node i and ending at node j. (reminder: a path is a sequence of nodes vi, .., Vk where successive nodes are adjacent. We can repeat nodes and edges in paths)

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