import java.util.Scanner; 

class Program01 {
 
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		System.out.println("Mátrix invertálása");
		
		System.out.print("Mátrix mérete: ");
		int size = in.nextInt();
		
		double[][] a = new double[size][size+size];
		
 
		//Az egységmátrix elkészítése
		for (int i = 0; i < size; i++) {
			for (int j = 0; j < size+size; j++) {
				if (j == i + size) {
					a[i][j] = 1;
				} else {
					a[i][j] = 0;
				}
			}
		}
 
		//Mátrix bekérése
		System.out.printf("\nÍrd be a %d X %d mátrixot:\n", size, size);
		for (int i = 0; i < size; i++) {
			for (int j = 0; j < size; j++) {				
				a[i][j] = in.nextDouble();
			}
		}
		
		
		if(det(a, size)==0) {
			System.out.println("Nem invertálható, mert a determinánsa 0");
		}else {		
			inverz(a, size);
			kiir(a, size);
		}
	}

	//Determináns számítása:
	static double det(double[][] a, int n) {
		double d = 1;
		for(int k=0; k<n; k++){
			for(int i=k+1; i<n; i++) {
				double g = a[i][k] / a[k][k];
				for(int j=k+1; j<n; j++) {
					a[i][j] = a[i][j] - g * a[k][j];
				}
			}
			d = d * a[k][k];
		}
		return d;
	}
	
	static void inverz(double[][] a, int size) {
		//Oszloponként változtatok
		for (int i = 0; i < size; i++) {
			reduction(a, size, i, i);
		}		
	}
	
	
	static void kiir(double[][] a, int size) {
		System.out.println("\nInverz mátrix");
		for (int i = 0; i < size; i++) {			
			for (int j = 0; j < size; j++) {
				System.out.printf("%8.2f", a[i][j + size]);
			}
			System.out.println();
		}
		
	}
	
	static void reduction(double a[][], int size, int pivot, int col) {
		double factor = a[pivot][col];

		for (int i = 0; i < 2 * size; i++) {
			a[pivot][i] /= factor;
		}
 
		for (int i = 0; i < size; i++) {
			if (i != pivot) {
				factor = a[i][col];
				for (int j = 0; j < 2 * size; j++) {
					a[i][j] = a[i][j] - a[pivot][j] * factor;
				}
			}
		}
	}
}