Example: Determinant of N x N Matrix in C

// Determinant of N x N Matrix
#include <stdio.h>
#include <math.h> // For pow function

// Function to get the cofactor of matrix[p][q] in temp matrix
void getCofactor(int matrix[10][10], int temp[10][10], int p, int q, int n) {
    int i = 0, j = 0;

    // Looping for each element of the matrix
    for (int row = 0; row < n; row++) {
        for (int col = 0; col < n; col++) {
            // Copying into temporary matrix only those elements which are not in given row and column
            if (row != p && col != q) {
                temp[i][j++] = matrix[row][col];

                // Row is full, go to next row
                if (j == n - 1) {
                    j = 0;
                    i++;
                }
            }
        }
    }
}

// Function to calculate determinant of a matrix recursively
int determinant(int matrix[10][10], int n) {
    int D = 0; // Initialize result

    // Base case : if matrix contains single element
    if (n == 1) {
        return matrix[0][0];
    }

    int temp[10][10]; // To store cofactors
    int sign = 1;      // To store sign multiplier

    // Iterate for each element of the first row
    for (int f = 0; f < n; f++) {
        // Getting Cofactor of matrix[0][f]
        getCofactor(matrix, temp, 0, f, n);
        D += sign * matrix[0][f] * determinant(temp, n - 1);

        // Term is multiplied by (-1)^(1+col_index)
        sign = -sign;
    }

    return D;
}

// Function to display the matrix
void displayMatrix(int matrix[10][10], int n) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            printf("%d ", matrix[i][j]);
        }
        printf("\n");
    }
}

int main() {
    // Step 1: Define an N x N matrix and its size
    int matrix1[10][10] = {
        {1, 2, 3},
        {4, 5, 6},
        {7, 8, 9}
    };
    int n1 = 3;

    // Step 2: Calculate its determinant
    printf("Matrix 1 (%dx%d):\n", n1, n1);
    displayMatrix(matrix1, n1);
    printf("Determinant = %d\n", determinant(matrix1, n1));

    printf("\n");

    int matrix2[10][10] = {
        {1, 0, 2, -1},
        {3, 0, 0, 5},
        {2, 1, 4, -3},
        {1, 0, 5, 0}
    };
    int n2 = 4;

    printf("Matrix 2 (%dx%d):\n", n2, n2);
    displayMatrix(matrix2, n2);
    printf("Determinant = %d\n", determinant(matrix2, n2));

    printf("\n");

    int matrix3[10][10] = {
        {6, 1, 1},
        {4, -2, 5},
        {2, 8, 7}
    };
    int n3 = 3;

    printf("Matrix 3 (%dx%d):\n", n3, n3);
    displayMatrix(matrix3, n3);
    printf("Determinant = %d\n", determinant(matrix3, n3));

    return 0;
}