/**
 * Inverse a matrix.
 * 
 * @author Small_Light
 * @version InverseMatrix 0.1
 */
import java.util.Scanner;

public class InverseMatrix {
    public static void main(String args[]) {
        Scanner s = new Scanner(System.in);
//        System.out.println("    Please print the row of your mathix : ");
        System.out.println("    请输入矩阵的行数 : ");
        int row = s.nextInt();
//        System.out.println("    Please print  your mathix : ");
        System.out.println("    请输入你的矩阵: ");

        double[][] matrix_old = new double[row][row];
        double[][] matrix_new = new double[row][row];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < row; j++) {
                matrix_old[i][j] = s.nextInt();
                matrix_new[i][j] = 0;
                if (i == j) {
                    matrix_new[i][j] = 1;
                }
            }
        }

        // **************以上内容完成矩阵的读取并且创建单位矩阵**************
        double temp;// col =1;j=2~row
        for (int col = 0; col < row; col++) {// col表示为处理到第几列
            for (int j = col + 1; j < row; j++) {// J标记为第几行
                temp = -matrix_old[j][col] / matrix_old[col][col];
                for (int i = 0; i < row; i++) {// 单独处理第J行的每一个元素
                    matrix_old[j][i] = matrix_old[j][i] + matrix_old[col][i]
                            * temp;
                    matrix_new[j][i] = matrix_new[j][i] + matrix_new[col][i]
                            * temp;
                }
            }
        }
        // 处理成为了上阶梯矩阵
        for (int i = 0; i < row; i++) {// i为行数，J为列数
            for (int j = 0; j < row; j++) {
                if (i < j) {
                    temp = matrix_old[i][j];
                    matrix_old[i][j] = matrix_old[j][i];
                    matrix_old[j][i] = temp;
                    temp = matrix_new[i][j];
                    matrix_new[i][j] = matrix_new[j][i];
                    matrix_new[j][i] = temp;
                }
            }
        }
        for (int col = 0; col < row; col++) {// col表示为处理到第几列
            for (int j = col + 1; j < row; j++) {// J标记为第几行
                temp = -matrix_old[j][col] / matrix_old[col][col];
                for (int i = 0; i < row; i++) {// 单独处理第J行的每一个元素
                    matrix_old[j][i] = matrix_old[j][i] + matrix_old[col][i]
                            * temp;
                    matrix_new[j][i] = matrix_new[j][i] + matrix_new[col][i]
                            * temp;
                }
            }
        }
        for (int i = 0; i < row; i++) {
            temp = matrix_old[i][i];

            for (int q = 0; q < row; q++) {
                matrix_old[i][q] = matrix_old[i][q] / temp;
                matrix_new[i][q] = matrix_new[i][q] / temp;

            }
        }
//        System.out.println("The inverse mathix is : ");
        System.out.println("该矩阵的逆矩阵是  : ");
        show(matrix_new);

    }

    public static void show(double[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                System.out.printf("%.4f\t",matrix[i][j] );
            }
            System.out.println();
        }

    }
}