Question $4$: We are given a directed graph G$($V$,$ E$)$ with vertices $\{1,2....,$ n$\},$ represented by an n $\backslash$times n matrix A so that A$[$i$,$ j$]=1$ if there is an edge from j to i in E$.$Give an algorithm that checks if there is a vertex v so that for every u $=$ v$,$ u $7->$ v in E$.$

Remarks: All the graphs here are without self loops and parallel or anti$-$parallel edges.In all the algorithms, always explain their correctness and analyze their complexity. The complexity should be as small as possible. A correct algorithm with large complexity, may be not good. You are not allowed to write programs but can wrire in psudocode.