# Determinant of a Matrix in C++ Program

C++Server Side ProgrammingProgramming

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;
}
if (n == 2) {
return (matrix * matrix) - (matrix * matrix);
}
int temp[N][N], sign = 1;
for (int i = 0; i < n; i++) {
subMatrix(matrix, temp, 0, i, n);
determinant += sign * matrix[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.