#include <iostream>

using namespace std;

void nhap(int &n) {
	do {
		cout<<"Nhap n: "; cin>>n;
		if (n < 3 || n > 10) cout<<"\nNhap 3 <= n <= 10";
	} while (n < 3 || n > 10);
}

void nhap_ma_tran(int a[][10], int n) {
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			cout<<"Nhap a["<<i<<","<<j<<"] = ";
			cin>>a[i][j];
		}
	}
}

void hien_thi(int a[][10], int n) {
	cout<<"Ma tran A:"<<endl;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			cout<<"\t"<<a[i][j];
		}
		cout<<endl;
	}
}

void ma_tran_don_vi(int a[][10], int n) {
	bool check = true;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			if (i != j && a[i][j] != 0) check = false;
			if (i == j && a[i][j] != 1) check = false;
		}
	}
	if (check)
		cout<<"Ma tran A la ma tran don vi"<<endl;
	else
		
		cout<<"Ma tran A khong phai ma tran don vi"<<endl;
}

void dinh_thuc_ma_tran(int a[][10], int n) {
	int det = 1;
	float x;
	for (int i = 0; i < n-1; i++) {
        if (a[i][i] == 0) {
            int k = i+1;
            while (k < n && a[k][i] == 0) k++;
            if (k > n-1) {
                det = 0;
                break;
            } else {
                det = -det;
                for (int j = i; j < n; j++) {
                    int tmp = a[i][j];
                    a[i][j] = a[k][j];
                    a[k][j] = tmp;
                }
            }
        }
        for (int k = i+1; k < n; k++) {
            float x = -a[k][i]/a[i][i];
            for (int j = i; j < n; j++) a[k][j] += x*a[i][j];
        }
    }
    for (int i = 0; i < n; i++) det *= a[i][i];
    cout<<"Dinh thuc cua A = "<<det<<endl;
}

int main() {
	int n;
	int a[10][10];
	nhap(n);
	nhap_ma_tran(a,n);
	hien_thi(a,n);
	ma_tran_don_vi(a,n);
	dinh_thuc_ma_tran(a,n);
	return 0;
}