package Maths;
import java.util.*;

/* 
* @author Ojasva Jain
* Determinant of Matrix Wikipedia link : https://en.wikipedia.org/wiki/Determinant
*/
public class DeterminantOfMatrix
{
 // Determinant calculator
 //@return determinant of the input matrix
 static int determinant(int a[][], int n)
 {
 int det = 0, sign = 1, p = 0, q = 0;
 if(n==1)
 {
 det = a[0][0];
 }
 else
 {
 int b[][] = new int[n-1][n-1];
 for(int x = 0 ; x < n ; x++)
 {
 p=0;q=0;
 for(int i = 1;i < n; i++)
 {
 for(int j = 0; j < n;j++)
 {
 if(j != x)
 {
 b[p][q++] = a[i][j];
 if(q % (n-1) == 0)
 {
 p++;
 q=0;
 }
 }
 }
 }
 det = det + a[0][x] *determinant(b, n-1) * sign;
 sign = -sign;
 }
 }
 return det;
 }
 //Driver Method
 public static void main(String [] args){
 Scanner in = new Scanner(System.in);
 //Input Matrix
 System.out.println("Enter matrix size (Square matrix only)");
 int n = in.nextInt();
 System.out.println("Enter matrix");
 int a [][] = new int [n][n];
 for(int i=0;i<n;i++){
 for(int j=0;j<n;j++){
 a[i][j] = in.nextInt();
 }
 }
 System.out.println(determinant(a, n));
 }
}