写一段C++代码使用 Vector 类和定义派生类 Matrix实现n阶矩阵的基本算术运算

好的，以下是一段使用 Vector 类和 Matrix 派生类实现基本矩阵算术运算的 C++ 代码：

#include <iostream>
#include <vector>

using namespace std;

class Matrix : public vector<vector<int>> {
public:
    Matrix(int n) : vector<vector<int>>(n, vector<int>(n)) {}

    Matrix operator+(const Matrix& other) const {
        Matrix result(size());
        for (int i = 0; i < size(); i++) {
            for (int j = 0; j < size(); j++) {
                result[i][j] = (*this)[i][j] + other[i][j];
            }
        }
        return result;
    }

    Matrix operator-(const Matrix& other) const {
        Matrix result(size());
        for (int i = 0; i < size(); i++) {
            for (int j = 0; j < size(); j++) {
                result[i][j] = (*this)[i][j] - other[i][j];
            }
        }
        return result;
    }

    Matrix operator*(const Matrix& other) const {
        Matrix result(size());
        for (int i = 0; i < size(); i++) {
            for (int j = 0; j < size(); j++) {
                for (int k = 0; k < size(); k++) {
                    result[i][j] += (*this)[i][k] * other[k][j];
                }
            }
        }
        return result;
    }

    void print() const {
        for (int i = 0; i < size(); i++) {
            for (int j = 0; j < size(); j++) {
                cout << (*this)[i][j] << " ";
            }
            cout << endl;
        }
    }
};

int main() {
    Matrix a(3);
    a[0][0] = 1;
    a[0][1] = 2;
    a[0][2] = 3;
    a[1][0] = 4;
    a[1][1] = 5;
    a[1][2] = 6;
    a[2][0] = 7;
    a[2][1] = 8;
    a[2][2] = 9;

    Matrix b(3);
    b[0][0] = 9;
    b[0][1] = 8;
    b[0][2] = 7;
    b[1][0] = 6;
    b[1][1] = 5;
    b[1][2] = 4;
    b[2][0] = 3;
    b[2][1] = 2;
    b[2][2] = 1;

    Matrix c = a + b;
    c.print();

    Matrix d = a - b;
    d.print();

    Matrix e = a * b;
    e.print();

    return 0;
}

这段代码定义了一个 Matrix 类，继承自 vector<vector<int>>，表示一个 n 阶矩阵。类中重载了加、减、乘三个运算符，分别实现了矩阵加、减、乘三种基本算术运算。还定义了一个 print() 方法，用于输出矩阵。在 main() 函数中，我们创建了两个 3 阶矩阵 a 和 b，并对它们进行加、减、乘运算，最后输出结果。