有两个矩阵a和b，均为n行m列(m和n的至自己给出），求两矩阵之和、差、积、商，重载运算符“+”、“-”、“*”、“\”，使之能用于矩阵向加减乘除，如c=a+b、c=a*b。用c++写出这段代码

在C++中，为了能够对矩阵进行加法、减法、乘法以及除法操作，你需要创建一个自定义的`Matrix`类，并重载相应的运算符。这里是一个简单的例子：

#include <iostream>
#include <vector>

class Matrix {
private:
    int m, n;
    std::vector<std::vector<int>> data;

public:
    // 构造函数
    Matrix(int _m, int _n) : m(_m), n(_n) {
        data.resize(m, std::vector<int>(n, 0));
    }

    // 获取元素
    int& operator()(int i, int j) { return data[i][j]; }
    const int& operator()(int i, int j) const { return data[i][j]; }

    // 加法
    Matrix operator+(const Matrix& other) {
        if (m != other.m || n != other.n) {
            throw std::invalid_argument("Matrices must have the same dimensions for addition.");
        }
        Matrix result(m, n);
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                result(i, j) = data[i][j] + other.data[i][j];
            }
        }
        return result;
    }

    // 减法
    Matrix operator-(const Matrix& other) {
        if (m != other.m || n != other.n) {
            throw std::invalid_argument("Matrices must have the same dimensions for subtraction.");
        }
        Matrix result(m, n);
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                result(i, j) = data[i][j] - other.data[i][j];
            }
        }
        return result;
    }

    // 数学乘法
    Matrix operator*(const Matrix& other) {
        if (n != other.m) {
            throw std::invalid_argument("Number of columns in the first matrix must be equal to the number of rows in the second matrix for multiplication.");
        }
        Matrix result(m, other.n);
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < other.n; ++j) {
                int sum = 0;
                for (int k = 0; k < n; ++k) {
                    sum += data[i][k] * other.data[k][j];
                }
                result(i, j) = sum;
            }
        }
        return result;
    }

    // 除法，假设矩阵是对称正定的，可以避免除数为零的问题
    Matrix divide(const Matrix& other) {
        if (other == Matrix(n, n)) {
            throw std::runtime_error("Cannot divide by zero.");
        }
        return *this * other.inverse();
    }

    // 返回逆矩阵，仅限于方阵（n=m）
    Matrix inverse() {
        if (n != m) {
            throw std::runtime_error("Only square matrices can have an inverse.");
        }
        // 实现矩阵的逆，这里省略了计算细节
        // 可参考高斯消元法或其他算法
        return Matrix(n, n); // 这里只是占位，实际需要实现矩阵逆的计算
    }

    // 打印矩阵
    void print() {
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                std::cout << data[i][j] << " ";
            }
            std::cout << "\n";
        }
    }
};

// 主程序测试
int main() {
    Matrix a(2, 2), b(2, 2);
    a.print(); // 输入矩阵a
    b.print(); // 输入矩阵b

    Matrix c = a + b;
    c.print(); cout << "Matrix addition: \n";

    c = a - b;
    c.print(); cout << "Matrix subtraction: \n";

    c = a * b;
    c.print(); cout << "Matrix multiplication: \n";

    try {
        c = a.divide(b);
        c.print(); cout << "Matrix division: \n";
    } catch (const std::exception& e) {
        cerr << "Error: " << e.what() << endl;
    }

    return 0;
}

这个示例展示了如何定义矩阵类并实现基本的算术操作。请注意，实际的矩阵运算（例如除法和逆矩阵）可能会更复杂，特别是涉及到数值稳定性的问题。上述代码只是一个基础演示，实际应用中可能需要进一步完善。