Example: Determinant of 3x3 Matrix in C++

// Determinant of 3x3 Matrix
#include <iostream>
using namespace std;

int main() {
    // Step 1: Declare and initialize a 3x3 matrix
    // You can also take input from the user here.
    int matrix[3][3] = {
        {1, 2, 3},
        {4, 5, 6},
        {7, 8, 9}
    };

    // Step 2: Print the matrix for verification
    cout << "The 3x3 Matrix is:" << endl;
    for (int i = 0; i < 3; ++i) {
        for (int j = 0; j < 3; ++j) {
            cout << matrix[i][j] << " ";
        }
        cout << endl;
    }

    // Step 3: Calculate the determinant using the formula
    // For a matrix:
    // | a b c |
    // | d e f |
    // | g h i |
    // Determinant = a(ei - fh) - b(di - fg) + c(dh - eg)

    int det = 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 4: Display the result
    cout << "\nDeterminant of the 3x3 matrix is: " << det << endl;

    return 0;
}