Title Introduction

Given a matrix of n*n, output its determinant value and inverse matrix.

Explain

When reviewing linear algebra at the end of the term, I found that I always find the inverse matrix wrong, so I just wrote a program to realize it.. As for whether it's all or all or something Come and fill this hole later.
Gauss elimination method can solve linear equations with a little modification of the code, and it is not difficult to judge no solution / infinite solution. As for finding the free unknown quantity and outputting any solution I haven't thought about it yet. I'll fill it in later

#include <bits/stdc++.h>
using namespace std;

const double eps = 1e-6;
const int N = 12;

void gauss(double a[][N], double b[], double x[], int n)
{
    int i;
    double s;
    for (int k = 1; k <= n; ++k) {
        for (i = k; i <= n && fabs(a[i][k]) < eps; ++i);
        if (i != k) {
            for (int j = k; j <= n; ++j)
                swap(a[i][j], a[k][j]);
            swap(b[i], b[k]);
        }
        for (i = k+1; i <= n; ++i) {
            s = a[i][k] / a[k][k];
            for (int j = k; j <= n; ++j)
                a[i][j] -= a[k][j] * s;
            b[i] -= b[k] * s;
        }
    }
    for (i = n; i >= 1; --i) {
        s = b[i];
        for (int j = i+1; j <= n; ++j)
            s -= x[j] *a[i][j];
        x[i] = s / a[i][i];
        if (fabs(x[i]) < eps) x[i] = 0;
    }
}

int main()
{
    double a[N][N], b[N], x[N], mt[N][N], mk[N][N];
    int n;
    cin >> n;
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j <= n; ++j) {
            cin >> mk[i][j];
            a[i][j] = mk[i][j];
        }
        b[i] = 0;
    }
    gauss(a, b, x, n);
    double det = 1;
    for (int i = 1; i <= n; ++i)
        det *= a[i][i];
    if (fabs(det) < eps) det = 0;
    printf("%0.2f\n", det);
    for (int k = 1; k <= n; ++k) {
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= n; ++j)
                a[i][j] = mk[i][j];
            b[i] = 0;
        }
        b[k] = 1;
        gauss(a, b, x, n);
        for (int i = 1; i <= n; ++i)
            mt[i][k] = x[i];
    }
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j < n; ++j)
            printf("%0.2f ", mt[i][j]);
        printf("%0.2f\n", mt[i][n]);
    }
    return 0;
}