G=(V,E) has n vertices.
(V_{i},V_{j}) can have a path more than 1 edges
if that is the case we will take maximum length path
A[j,k] = max(A[j,k], A[j,i] + A[i,k]);
Now take an example with 2 vertices
Here we can check option B) A[1,1]=0<(n-1)=2-1=1
So, this option false
Now, take another graph where loop is present
In option C)says A[j,k] contains the longest path length from j to k
But if there is a loop present then longest path will contain the loop.
See here A[1,1]=1->2->1
But according to algorithm we can work with only simple path
So, this option also false.
Now, A) option
See, A[1,2] max length of path is 3, as 1 contain a self loop.
A[1,2]=3>2=n [where n is number of vertices
Atlast option D) If there exists a path from j to k, every simple path from j to k contains at most A[j,k] edges
it is completely TRUE. As it is clearly mention simple path.
So, Ans D)