(1) Consider a graph whose adjacenty matrix is 1 A= 0 1 1 0 Find the number of paths of length 4 from 1 to 3. (2) (a) Find (without explicit calculation) an example of a 4 x 4 nonzero adjacenty matrix such that all powers of this matrix beyond the 10th power are zero. Justify briefly. (b) Show that the 8th power of any such matrix must also be zero. (c) Is it true that the cube of any such matrix also has to be zero? (3) Draw the graph of the relation R = ((a, b) | 0 3) on the set (1, 2,3} using Boolean powers of the adjacenty matrix