$[$This main motivation for this problem is to practice designing algorithms and pseudocode as well as

interacting with graphs using adjacency matrices.$]$

An adjacency matrix for an undirected graph with vertices labeled $1$ through $n$ is a symmetric matrix

such that entry $(i,j)$ is $1$ if there is an edge between vertex i and vertex $j$ and $0$ otherwise.

Example: Here is a graph and its adjacency matrix.

$([0,1,1,0,0,0],[1,0,0,1,0,0],[1,0,0,1,1,1],[0,1,1,0,1,1],[0,0,1,1,0,0],[0,0,1,1,0,0])$

A triangle in an undirected, simple graph is a set of three distinct vertices $x,y,z$ such that all pairs

are connected by an edge.

You are given $A,$ the adjacency matrix of an undirected graph $G.$

Design an algorithm that determines $($outputs True or False$)$ whether $G$ has a triangle or not.

$($You can present your algorithm using pseudocode. Please also include a runtime analysis.$)$