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## Homework Statement

Let A be the adjacency matrix for the graph G=(V,E)

(a) Show that A^3[i,i] equals twice the number of triangles containing vertex i. (A triangle is a cycle of length 3

(b) Find an interpretation for A^3[i,j] when i does not equal j similar to the above. Prove that your interpretation is correct.

## The Attempt at a Solution

I have no clue how to even start this proof...