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Java Program to Find the Determinant of a Matrix

Last Updated : 01 May, 2025
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The determinant of a matrix is a special calculated value that can only be calculated if the matrix has same number of rows and columns (square matrix). It is helpful in determining the system of linear equations, image processing, and determining whether the matrix is singular or non-singular.

In this article, we are going to learn the step-by-step procedure to calculate the determinant of a matrix and Java implementations using both recursive and non-recursive approaches.

Procedure to Calculate

  • First, we need to calculate the cofactor of all the elements of the matrix in the first row or first column.
  • Then, multiply each element of the first row or first column by their respective cofactor.
  • At last, we need to add them up with alternate signs.

Examples:

Determinant of 2*2 matrix:

[4, 3]
[2, 3]

= (4*3)-(3*2)
= 12-6
= 6


Determinant of 3*3 matrix:

[1, 3, -2]
[-1, 2, 1]
[1, 0, -2]

= 1(-4-0)-3(2-1)+(-2)(0-2)
= -4-3+4
= -3

Note:

  • The determinant of 1*1 matrix is the element itself.
  • The Cofactor of any element of the stated matrix can be calculated by eliminating the row and the column of that element from the matrix stated.

Let’s see an example to get a clear concept of the above topic.

Determinant of a Matrix in Java

Example 1: Finding the determinant of a matrix using recursion.

Java
// Java program to find
// Determinant of a matrix
// using recursion
class Geeks
{

    // Dimension of input square matrix
    static final int N = 2;

    // Function to get cofactor of
    // mat[p][q] in temp[][]. n is
    // current dimension of mat[][]
    static void getCofactor(int mat[][], int temp[][],
                            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 element which are
                // not in given row and column
                if (row != p && col != q) {
                    temp[i][j++] = mat[row][col];
                    
                    // Row is filled, so increase
                    // row index and reset col index
                    if (j == n - 1) {
                        j = 0;
                        i++;
                    }
                }
            }
        }
    }

    /* Recursive function for finding determinant
    of matrix. n is current dimension of mat[][]. */
    static int determinantOfMatrix(int mat[][], int n)
    {
        int D = 0; // Initialize result

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

        // To store cofactors
        int temp[][] = new int[N][N];

        // To store sign multiplier
        int sign = 1;

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

            // terms are to be added
            // with alternate sign
            sign = -sign;
        }

        return D;
    }

    // function for displaying the matrix 
    static void display(int mat[][], int row, int col)
    {
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++)
                System.out.print(mat[i][j]);

            System.out.print("\n");
        }
    }

    // Driver code
    public static void main(String[] args)
    {

        int mat[][] = { { 4, 3 }, { 2, 3 } };

        System.out.print("Determinant "
                         + "of the matrix is: "
                         + determinantOfMatrix(mat, N));
    }
}

Output
Determinant of the matrix is: 6

Time complexity: O(n3


Example 2: Non-recursive Implementation of finding determinant of a matrix.

Java
// Java program to find Determinant of a matrix
class Geeks
{

    // Dimension of input square matrix
    static final int N = 4;

    // Function to get determinant of matrix
    static int determinantOfMatrix(int mat[][], int n)
    {
        int num1, num2, det = 1, index,
                        total = 1; // Initialize result

        // temporary array for storing row
        int[] temp = new int[n + 1];

        // loop for traversing the diagonal elements
        for (int i = 0; i < n; i++) {
            index = i; // initialize the index

            // finding the index which has non zero value
            while (mat[index][i] == 0 && index < n) {
                index++;
            }
            if (index == n) // if there is non zero element
            {
                // the determinant of matrix as zero
                continue;
            }
            if (index != i) {
                
                // loop for swapping the diagonal element row
                // and index row
                for (int j = 0; j < n; j++) {
                    swap(mat, index, j, i, j);
                }
                // determinant sign changes when we shift
                // rows go through determinant properties
                det = (int)(det * Math.pow(-1, index - i));
            }

            // storing the values of diagonal row elements
            for (int j = 0; j < n; j++) {
                temp[j] = mat[i][j];
            }

            // traversing every row below the diagonal
            // element
            for (int j = i + 1; j < n; j++) {
                num1 = temp[i]; // value of diagonal element
                num2 = mat[j]
                          [i]; // value of next row element

                // traversing every column of row
                // and multiplying to every row
                for (int k = 0; k < n; k++) {
                    
                    // multiplying to make the diagonal
                    // element and next row element equal
                    mat[j][k] = (num1 * mat[j][k])
                                - (num2 * temp[k]);
                }
                total = total * num1; // Det(kA)=kDet(A);
            }
        }

        // multiplying the diagonal elements to get
        // determinant
        for (int i = 0; i < n; i++) {
            det = det * mat[i][i];
        }
        return (det / total); // Det(kA)/k=Det(A);
    }

    static int[][] swap(int[][] arr, int i1, int j1, int i2,
                        int j2)
    {
        int temp = arr[i1][j1];
        arr[i1][j1] = arr[i2][j2];
        arr[i2][j2] = temp;
        return arr;
    }

    // Driver code
    public static void main(String[] args)
    {
        int mat[][] = { { 1, 0, 2, -1 },
                        { 3, 0, 0, 5 },
                        { 2, 1, 4, -3 },
                        { 1, 0, 5, 0 } };

        // Function call
        System.out.printf(
            "Determinant of the matrix is: %d",
            determinantOfMatrix(mat, N));
    }
}

Output
Determinant of the matrix is: 30

Time complexity: O(n3



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