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));
    }
}