C Program to check matrix is magic square or not

A magic square is a square matrix in which the sum of every row, every column, and both main diagonals is the same number (called the magic constant). This C program reads a square matrix and checks whether it is a magic square.

Example:

8  1  6
3  5  7
4  9  2

Every row, column and diagonal here adds up to 15, so this is a magic square (it’s the classic 3×3 “Lo Shu” square).

The Program

#include <stdio.h>

#define MAX 20

int main(void)
{
    int a[MAX][MAX], n, i, j, sum, target, magic = 1;

    printf("Enter the order of the square matrix (n) : ");
    scanf("%d", &n);

    printf("Enter the %d x %d matrix elements:\n", n, n);
    for (i = 0; i < n; i++)
        for (j = 0; j < n; j++)
            scanf("%d", &a[i][j]);

    /* The magic constant is the sum of the first row. */
    target = 0;
    for (j = 0; j < n; j++)
        target += a[0][j];

    /* Check every row. */
    for (i = 0; i < n && magic; i++) {
        sum = 0;
        for (j = 0; j < n; j++)
            sum += a[i][j];
        if (sum != target) magic = 0;
    }

    /* Check every column. */
    for (j = 0; j < n && magic; j++) {
        sum = 0;
        for (i = 0; i < n; i++)
            sum += a[i][j];
        if (sum != target) magic = 0;
    }

    /* Check both diagonals. */
    if (magic) {
        int d1 = 0, d2 = 0;
        for (i = 0; i < n; i++) {
            d1 += a[i][i];
            d2 += a[i][n - 1 - i];
        }
        if (d1 != target || d2 != target) magic = 0;
    }

    if (magic)
        printf("The given matrix is a magic square.\n");
    else
        printf("The given matrix is NOT a magic square.\n");

    return 0;
}

How the Program Works

• We take the sum of the first row as the target (magic constant) that everything else must match.
• Three checks follow: every row sum, every column sum, and both diagonal sums must equal target.
• The magic flag starts at 1 and is set to 0 the moment any sum doesn’t match, so we can stop early.
• This corrected version checks both diagonals (the original only checked one) and uses a standard int main(void) instead of the old void main().

Sample Output

Enter the order of the square matrix (n) : 3
Enter the 3 x 3 matrix elements:
8 1 6
3 5 7
4 9 2
The given matrix is a magic square.

For more on 2D arrays and matrices in C, The C Programming Language by Kernighan and Ritchie is the classic reference — find it on Amazon.

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