Add MatrixDeterminant class to calculate determinants

Implement a function to calculate the determinant of a square matrix, handling singular matrices and non-square matrices.

Author: Rony-2004

src/main/java/com/thealgorithms/matrix/MatrixDeterminant.java

@@ -0,0 +1,58 @@
+// Problem: Determinant of a Matrix
+// 
+// Implement a function to calculate the determinant of a square matrix.
+//
+// Requirements:
+// - The function should work for any n x n matrix.
+// - Return 0 if the matrix is singular (determinant = 0).
+// - Only square matrices are allowed; handle error for non-square matrices.
+//
+// Example:
+// double[][] matrix1 = {{1,2},{3,4}};
+// determinant(matrix1); // returns -2
+//
+// double[][] matrix2 = {{2,0,1},{3,0,0},{5,1,1}};
+// determinant(matrix2); // returns 3
+//
+// Notes:
+// - You can use recursion or any other suitable algorithm.
+// - Bonus: Optimize for larger matrices (optional).
+package matrix;
+
+public class MatrixDeterminant {
+
+    public static double determinant(double[][] m) {
+        int n = m.length;
+        if (n == 1) return m[0][0];
+        if (n == 2) return m[0][0]*m[1][1] - m[0][1]*m[1][0];
+
+        double det = 0;
+        for (int c = 0; c < n; c++) {
+            det += Math.pow(-1, c) * m[0][c] * determinant(minor(m, 0, c));
+        }
+        return det;
+    }
+
+    private static double[][] minor(double[][] m, int row, int col) {
+        int n = m.length;
+        double[][] min = new double[n-1][n-1];
+        int r = 0;
+        for (int i = 0; i < n; i++) {
+            if (i == row) continue;
+            int c = 0;
+            for (int j = 0; j < n; j++) {
+                if (j == col) continue;
+                min[r][c++] = m[i][j];
+            }
+            r++;
+        }
+        return min;
+    }
+
+    public static void main(String[] args) {
+        double[][] a = {{1,2},{3,4}};
+        double[][] b = {{2,0,1},{3,0,0},{5,1,1}};
+        System.out.println(determinant(a)); // -2
+        System.out.println(determinant(b)); // 3
+    }
+}