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The following questions are related to adjacency matrix representation of graphs. (a) Write down the adjacency matrix A of the following undirected graph. (b) Let P_ij be the number of paths of length 2 in the abovementioned graph that start from vertex i and finish in vertex j. For example, P_23 = 1 because there is only one path of length 2 that connects 2 and 3: 2-4-3. The same edge can be used many times in each path (i.e., 2-4-2 is a path). Write down the matrix P, i.e., the number of paths of length 2 for each pair of vertices