Example: Determinant of 3x3 Matrix in C

// Determinant of 3x3 Matrix
#include <stdio.h>

// Function to calculate determinant of a 2x2 matrix (helper for 3x3)
int determinant2x2_helper(int matrix[2][2]) {
    return (matrix[0][0] * matrix[1][1]) - (matrix[0][1] * matrix[1][0]);
}

// Function to calculate determinant of a 3x3 matrix
int determinant3x3(int matrix[3][3]) {
    int det = 0;

    // Cofactor for first element (0,0)
    // Submatrix: | matrix[1][1] matrix[1][2] |
    //            | matrix[2][1] matrix[2][2] |
    int submatrix1[2][2] = {
        {matrix[1][1], matrix[1][2]},
        {matrix[2][1], matrix[2][2]}
    };
    det += matrix[0][0] * determinant2x2_helper(submatrix1);

    // Cofactor for second element (0,1) with negative sign
    // Submatrix: | matrix[1][0] matrix[1][2] |
    //            | matrix[2][0] matrix[2][2] |
    int submatrix2[2][2] = {
        {matrix[1][0], matrix[1][2]},
        {matrix[2][0], matrix[2][2]}
    };
    det -= matrix[0][1] * determinant2x2_helper(submatrix2);

    // Cofactor for third element (0,2)
    // Submatrix: | matrix[1][0] matrix[1][1] |
    //            | matrix[2][0] matrix[2][1] |
    int submatrix3[2][2] = {
        {matrix[1][0], matrix[1][1]},
        {matrix[2][0], matrix[2][1]}
    };
    det += matrix[0][2] * determinant2x2_helper(submatrix3);

    return det;
}

int main() {
    // Step 1: Define a 3x3 matrix
    int matrix[3][3] = {
        {1, 2, 3},
        {4, 5, 6},
        {7, 8, 9}
    };

    // Step 2: Calculate its determinant
    int det = determinant3x3(matrix);

    // Step 3: Print the result
    printf("The 3x3 matrix:\n");
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            printf("%d ", matrix[i][j]);
        }
        printf("\n");
    }
    printf("Determinant = %d\n", det);

    // Another example
    int matrix2[3][3] = {
        {6, 1, 1},
        {4, -2, 5},
        {2, 8, 7}
    };
    det = determinant3x3(matrix2);
    printf("\nThe second 3x3 matrix:\n");
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            printf("%d ", matrix2[i][j]);
        }
        printf("\n");
    }
    printf("Determinant = %d\n", det);


    return 0;
}