Determinant_of_Matrix.java

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

	// 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));
	}
}