3. Consider the directed acyclic graph (DAG) shown below. (a) Write down the adjacency matrix A corresponding to the ordering of the vertices given by alphabetical order: a, b, c, d, e, ƒ. (b) For the matrix A found in part (a), compute the matrix (I – A)-1, where I denotes the 6 x 6 identity matrix, and show all your work. (Hint: it is much easier to do this by counting paths, rather than using linear algebra! But if you insist on doing this using linear algebra, you must still show all your work.) (c) Find all permutations of the set of vertices {a, b, c, d, e, ƒ} such that the associ- ated adjacency matrix is strictly lower triangular.

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