A directed graph $G$ has $5$ vertices, numbered $1$ through $5.$ The $55$ matrix $A$ is the adjacency matrix for $G.$ The matrices $A2$ and $A3$ are given below.

$A^2=([0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,1,0,0],[0,0,1,0,1]),A^3=([0,0,0,1,0],[0,0,0,0,1],[1,0,1,0,0],[0,1,0,1,0],[0,0,1,0,1])$

Which edge is not in the transitive closure of G$?$

$(1,3)$

$(2,4)$

$(4,5)$

$(5,5)$