Chapter 11.2, Problem 9E

(a)

To determine

The value of A. If A be the adjacency matrix of the illustrated graph

(b)

To determine

The value of $(3,3)$ and $(1,4)$ entries of $A^2$ without calculating the matrix $A^2$

(c)

To determine

The $(4,2)$ entry $A^3$ and the $(1,3)$ entry of $A^4$ without calculating of $A^4$ the matrix $A^2$.

(d)

To determine

Whether the digraph is strongly connected or not.

(e)

To determine

The digraph is Eulerian or not.