Depth First Search Implementation (iterative)
Advice 1 (Space around binary operators)

Matrix=matrix


PEP-8 requires one space before a binary operator and after it:

Matrix = matrix


Advice 2 (Variable names should start from a lowercase letter)

Once again, you have a variable called Matrix. This applies to the function name DFS as well; I suggest you rename it to depth_first_search.

Advice 3

You print intermediate progress in your algorithm. Never do this. Think about what happens when your friend reuses your implementation: he or she will get overwhelmed with all that output that has no value. Also, it might slow down the execution of your algorithm, since printing goes down the chain to the very kernel. If you need to print anything, modify your algorithm to return a data structure which can do that, but let it do its work silently.

Advice 4

Your implementation seems to run in \$\Theta(V^2)\$ time. I suggest you convert the adjacency matrix to an adjacency list and input that list to your depth first search; this will bring down complexity to \$\Theta(E + V)\$, which is more efficient on sparse graphs (where \$E = o(V^2)\$).

Alternative implementation

Putting all together, I had this in mind:

from collections import deque


def adjacency_matrix_to_adjacency_list(adjacency_matrix):
    map = dict()
    j = 0

    for i in range(len(adjacency_matrix)):
        map[i] = []

    for adjacency_matrix_row in adjacency_matrix:
        for i in range(len(adjacency_matrix_row)):
            current_entry = adjacency_matrix_row[i]

            if current_entry == 1:
                map[j].append(i)

        j += 1

    return map


def depth_first_search(adjacency_matrix, source_node):
    open = deque([source_node])
    parents = {source_node: None}

    while open:
        current_node = open.pop()

        for child_node in adjacency_matrix[current_node]:
            if child_node not in parents.keys():
                parents[child_node] = current_node
                open.append(child_node)

    return parents