Problem $4$: $(15$ points$)$

Let $G=(V,E)$ be the following directed graph: $V=\{1,2,3,4,5\},$ and $,(1,5),(4,5),(3,5).$

a$)$ Draw $G$ and give its adjacency matrix $A.$

b$)$ Compute the indegree and outdegree of each node.

c$)$ For every node, list all the nodes reachable from it$.$ Is G strongly connected?

d$)$ Compute $A^2,A^3,A^4,A^5$ and $B=I_5+A+A^2+A^3+A^4+A^5.$

e$)$ Based on the matrix $B,$ how can you conclude if $G$ is strongly connected or not?