vet = (int**)malloc( (N)*(N)*sizeof(int*) );

  for (i = 0; i < N; i++)
    for (j = 0; j < N; j++)
      scanf("%d", &vec[i][j]);

#include <stdio.h>
#include <stdlib.h>

char *IAm;

/* For this demo we dn't care about the argument being a power of 2; just > 0 */
int check(int N) {
	return(N > 0);
}

/* Calculate subscript into a vector for a simulated NxN array. */
int s(int N, int row, int col) {
	if(N < 0 || row < 0 || col < 0 || row >= N || col >= N) {
		fprintf(stderr, "%s: s(N=%d,row=%d,col=%d)\n",
		    IAm, N, row, col);
		fprintf(stderr, "%s: s(): Expect N>0, 0<=row<N, 0<=col<N\n",
		    IAm);
		exit(4);
	}
	return(row * N + col);
}

int main(int argc, char *argv[]) {
	int	i,
		j,
		N,
		result = 0,
		*vec;		/* Note *vec; not **vec. */

	IAm = argv[0];
	if (argc < 2) {
		fprintf(stderr, "Usage: %s N\n", argv[0]);
		exit(1);
	}

	/* ... how many numbers to read */
	N = atoi(argv[1]);
	/* check if N is a power of two; exit if not */
	if (! check(N)) {
		fprintf(stderr,
		    "%d is not a power of 2 as required.  Exiting.\n", N);
		exit(2);
	}

	vec = (int*)malloc( (N)*(N)*sizeof(int) ); /* int**->int*; int*->int */
	if ( vec == NULL ) {
		fprintf (stderr, "ERROR: not enough memory available!\n");
		exit(3);
	}

	for (i = 0; i < N; i++)
		for (j = 0; j < N; j++)
			scanf("%d", &vec[s(N, i, j)]); /* [i][j]->[s(N,i,j)] */

	printf("\nOriginal array:\n");  /* Trailing space removed from format.*/
	for (i = 0; i < N; i++) {
		for (j = 0; j < N; j++)
			printf("%d ", vec[s(N, i, j)]);
		printf("\n");
	}

/* Without knowing what check_property() does, I don't know if:
**	check_property(vec[i], 0, N-1)
** in the following just needs to be changed to:
**	check_property(&vec[i * N], 0, N-1)
** or if something much deeper needs to be done.
*/
	/* Now process array; example below is to add numbers */
//	for (i = 0; i < N; i++) {
//		result = check_property(vec[i], 0, N-1);
//		printf("result[line %d]: %d\n", i, result);
//	}

	/* free memory */
	free(vec);

	exit(0);
}

./program 16

echo 11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44 | ./program 4

Original array:
11 12 13 14 
21 22 23 24 
31 32 33 34 
41 42 43 44