Determinant of a Matrix in C++ Program

In this tutorial, we are going to learn how to find the determinant of a matrix.

Let's see the steps to find the determinant of a matrix.

• Initialize the matrix.

• Write a function to find the determinant of the matrix.

  • If the size of the matrix is 1 or 2, then find the determinant of the matrix. It's a straightforward thing.

  • Initialize variables for determinant, submatrix, sign.

  • Iterate from 1 to the size of the matrix N.

  • Find the submatrix for the current matrix element.

    • All the elements that are not in the current element row and column

  • Add the product of the current element and its cofactor to the determinant.

  • Alter the sign.

• Print the determinant of the matrix.

Example

Let's see the code.

 Live Demo

#include <bits/stdc++.h> using namespace std; #define N 3 void subMatrix(int mat[N][N], int temp[N][N], int p, int q, int n) {    int i = 0, j = 0;    // filling the sub matrix    for (int row = 0; row < n; row++) {       for (int col = 0; col < n; col++) {          // skipping if the current row or column is not equal to the current          // element row and column          if (row != p && col != q) {             temp[i][j++] = mat[row][col];             if (j == n - 1) {                j = 0;                i++;             }          }       }    } } int determinantOfMatrix(int matrix[N][N], int n) {    int determinant = 0;    if (n == 1) {       return matrix[0][0];    }    if (n == 2) {       return (matrix[0][0] * matrix[1][1]) - (matrix[0][1] * matrix[1][0]);    }    int temp[N][N], sign = 1;    for (int i = 0; i < n; i++) {       subMatrix(matrix, temp, 0, i, n);       determinant += sign * matrix[0][i] * determinantOfMatrix(temp, n - 1);       sign = -sign;    }    return determinant; } int main() {    int mat[N][N] = {{2, 1, 3}, {6, 5, 7}, {4, 9, 8}};    cout << "Determinant: " << determinantOfMatrix(mat, N) << endl;    return 0; }

Output

If you execute the above program, then you will get the following result.

Determinant: 36

Conclusion

If you have any queries in the tutorial, mention them in the comment section.