Example: Determinant of a 3x3 Matrix in C

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

int main() {
    // Step 1: Declare a 3x3 matrix
    int matrix[3][3];
    int i, j;
    long determinant; // Using long for determinant to handle larger values

    // Step 2: Prompt the user to enter elements of the 3x3 matrix
    printf("Enter the elements of the 3x3 matrix:\n");
    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            printf("Enter element matrix[%d][%d]: ", i, j);
            scanf("%d", &matrix[i][j]);
        }
    }

    // Step 3: Display the entered matrix (optional, for verification)
    printf("\nThe entered 3x3 matrix is:\n");
    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            printf("%d\t", matrix[i][j]);
        }
        printf("\n");
    }

    // Step 4: Calculate the determinant using the cofactor expansion method
    // Formula: det = a(ei - fh) - b(di - fg) + c(dh - eg)
    // Here, a = matrix[0][0], b = matrix[0][1], c = matrix[0][2]
    // d = matrix[1][0], e = matrix[1][1], f = matrix[1][2]
    // g = matrix[2][0], h = matrix[2][1], i = matrix[2][2]
    determinant = matrix[0][0] * (matrix[1][1] * matrix[2][2] - matrix[1][2] * matrix[2][1]) -
                  matrix[0][1] * (matrix[1][0] * matrix[2][2] - matrix[1][2] * matrix[2][0]) +
                  matrix[0][2] * (matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0]);

    // Step 5: Print the calculated determinant
    printf("\nDeterminant of the 3x3 matrix = %ld\n", determinant);

    return 0;
}