During the DFS traversal, we can keep track of the visited nodes and the current path. If we encounter a node that has already been visited and is still on the current path, then we have detected a cycle.

```
function isCyclic(adj:number[][], v:number){
let helper:boolean[] = new Array<boolean>(v).fill(false);
let visited:boolean[] = new Array<boolean>(v).fill(false);
for(let i:number=0 ; i<v;i++){
console.log(visited);
if(visited[i] == false ){
//call DFS
const ans = DFS(adj, i, helper, visited);
if(ans==true) return true;
}
}
return false;
}
function DFS(adj:number[][], index:number,helper:boolean[], visited:boolean[]){
helper[index] = true;
visited[index] = true;
let neighbor = adj[index];
for(let k:number =0 ; k<neighbor.length;k++){
let curr = neighbor[k];
if(helper[curr]==true) return true;
if(visited[curr]==false){
let ans = DFS(adj,curr, helper, visited);
if(ans == true) return true;
}
}
helper[index] = false;
return false;
}
const matrix:number[][] = [[0,1],[1,2],[2,3],[3,4],[4,4]]
console.log(isCyclic(matrix, matrix.length))
```

This code is implementing a solution to detect cycles in a directed graph using Depth First Search (DFS) algorithm.

The `isCyclic`

function takes an adjacency matrix and the number of vertices as inputs. It initializes two arrays: `helper`

to keep track of nodes on the current path and `visited`

to keep track of visited nodes. It then loops through each unvisited node and calls the `DFS`

function on it. If the `DFS`

function returns true, indicating that a cycle is found, the `isCyclic`

function returns true. Otherwise, it continues to the next unvisited node.

The `DFS`

function takes the adjacency matrix, the index of the current node, and the `helper`

and `visited`

arrays as inputs. It first marks the current node as visited and adds it to the `helper`

array to keep track of nodes on the current path. It then loops through each neighbor of the current node and recursively calls itself on unvisited neighbors. If it encounters a neighbor that is already on the `helper`

array, it returns true to indicate the presence of a cycle. Otherwise, it continues to the next neighbor. After exploring all neighbors, the function removes the current node from the `helper`

array and returns false.

The code seems to be correct and will work for detecting cycles in a directed graph represented by an adjacency matrix. However, note that this implementation assumes that the graph is a simple directed graph with no self-loops. If the graph has self-loops or multiple edges between nodes, the implementation may need to be modified.