Pointing Array between functions

Hi everyone, I'm stuck here and I need help on how am I suppose to point the array to another function to edit.

This program is suppose to take in a matrix with side (NxN) and will output the matrix by adding the four nearby number together.

eg.
0 1 2
3 4 5
6 7 8

will output
8 12
20 24

The code works, but somehow at the second row, [1][0] it adds the new [0][0] and [0][1]...

Anybody would be kind enough to brainstorm with me?

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#include<iostream>
#include<string>
#include<cstdlib>
#include <iomanip>  

using namespace std;

int ask();
int initialize_matrix(int);
int is_positive_int(string);
int** iterative_calculate_result(int**, int);

/********************************************************************* 
 ** Function: main()
 ** Description: The main function that contains other functions
 ** Parameters: -
 ** Pre-Conditions: - 
 ** Post-Conditions: Runs the functions
 *********************************************************************/
int main() {
    int N;
	
    N = ask();
	initialize_matrix(N);

	
}

/********************************************************************* 
 ** Function: ask()
 ** Description: Asks for N from user
 ** Parameters: None
 ** Pre-Conditions: main() is being run
 ** Post-Conditions: Returns N to main()
 *********************************************************************/
int ask() {

    string Nstr;
	int pos, N;

    cout << "Enter N for Matrix (N x N): " << endl;
	cin >> Nstr;

	pos = is_positive_int(Nstr);
	
    if(pos == 1) {
	    N = atoi(Nstr.c_str());
	    return N; }
	else {
	    cout << "Error try again!" << endl;
		exit(1); }
	
}


/********************************************************************* 
 ** Function: is_positive_int(string Nstr)
 ** Description: Takes the string from ask() to check whether positive
 ** Parameters: Nstr
 ** Pre-Conditions: Nstr
 ** Post-Conditions: returns is positive or not
 *********************************************************************/
int is_positive_int(string Nstr) {

    for(int i = 0; i < Nstr.size(); i++ )
	{
	    if(Nstr.at(i) == '.' || Nstr.at(i) == '-')
		    return 0;
		else
		    return 1;
	}

}

/********************************************************************* 
 ** Function: initialize_matrix(int N)
 ** Description: Takes input for matrix and prints the matrix
 ** Parameters: N
 ** Pre-Conditions: N is positive 
 ** Post-Conditions: Prints the matrix
 *********************************************************************/
int initialize_matrix(int N) {

    int ROW = N, COL = N;
    int **mat;
    int k = 0;
	
	mat = new int*[ROW];
	for(int i = 0; i < ROW; i++)
	    mat[i] = new int[COL];

    for(int i = 0; i < ROW; i++)
	    for(int j = 0; j < COL; j++)
		    mat[i][j] = k++;
		
	for(int i = 0; i < N; i++) {
	    for(int j = 0; j < N; j++) {
		    cout << mat[i][j];
			cout << " ";
		}
		
		cout << endl;
    }	
	
    mat = iterative_calculate_result(mat, N);
	

}




/********************************************************************* 
 ** Function: iterative_calculate_result(int** arr, int N)
 ** Description: Calculates the 4 nearest number in the matrix
 ** Parameters: 
 ** Pre-Conditions: 
 ** Post-Conditions: 
 *********************************************************************/
 int** iterative_calculate_result(int** arr, int N) {

    int a, b, c ,d;
    int ** p;
	p = arr;

	for(int i = 0; i < N-1; i++) {
	    for(int j = 0; j < N-1; j++) {
		    a = arr[N-N][N-(N-j)];
			j++;
			b = arr[N-N][N-(N-j)];
			j--;
			i++;
			c = arr[N-(N-i)][N-(N-j)];
			j++;
			d = arr[N-(N-i)][N-(N-j)];
			j--;
			i--;
            arr[i][j] = a + b + c + d; 
			}
			
        }
	
	for(int i = 0; i < (N-1); i++) {
	    for(int j = 0; j < (N-1); j++) {
		    cout << arr[i][j];
			cout << " ";
		}
		
		cout << endl;
    }
	
	return arr;

 }
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