$)$ A directed graph is called strongly connected if for every i and j$,$ there is a path from vertex i to vertex j$.$

Select true or false.

$($a$)$ A graph with adjacency matrix A is strongly connected if and only if for some n$,$ the boolean power

A

$$n has all entries equal to $1.$

$($b$)$ A graph with adjacency matrix A is strongly connected if and only if for some n$,$ the boolean sum

I $`$ A$`$ A

$2``$ A

$$n

has all entries equal to $1.$

If the statement is true, you should be able to justify it$.$ Otherwise, you should be able to give a

counter$-$example. But you need not turn in the justification or counter$-$examples.