定义一个矩阵类 Matrix，均为 M 行 N 列，通过重载运算符“+”、“-”，“<<”,“>>”,“++”,“--”，“==”，“！=”来实现矩阵的相加、相减、输出、输入、自增、自减以及相等、不等的判断。

下面是一个简单的 Matrix 类的定义和重载运算符的实现：

#include <iostream>
using namespace std;

class Matrix {
private:
    int **data;  // 矩阵数据
    int rows, cols;  // 行数和列数

public:
    Matrix(int r, int c) : rows(r), cols(c) {
        data = new int*[rows];
        for (int i = 0; i < rows; i++) {
            data[i] = new int[cols];
            for (int j = 0; j < cols; j++) {
                data[i][j] = 0;
            }
        }
    }

    Matrix(const Matrix &other) { // 拷贝构造函数
        rows = other.rows;
        cols = other.cols;
        data = new int*[rows];
        for (int i = 0; i < rows; i++) {
            data[i] = new int[cols];
            for (int j = 0; j < cols; j++) {
                data[i][j] = other.data[i][j];
            }
        }
    }

    ~Matrix() {  // 析构函数
        for (int i = 0; i < rows; i++) {
            delete[] data[i];
        }
        delete[] data;
    }

    Matrix& operator=(const Matrix &other) {  // 赋值运算符
        if (this == &other) {
            return *this;
        }
        for (int i = 0; i < rows; i++) {
            delete[] data[i];
        }
        delete[] data;
        rows = other.rows;
        cols = other.cols;
        data = new int*[rows];
        for (int i = 0; i < rows; i++) {
            data[i] = new int[cols];
            for (int j = 0; j < cols; j++) {
                data[i][j] = other.data[i][j];
            }
        }
        return *this;
    }

    Matrix operator+(const Matrix &other) const {  // 矩阵相加
        if (rows != other.rows || cols != other.cols) {
            throw invalid_argument("Matrix sizes do not match.");
        }
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result.data[i][j] = data[i][j] + other.data[i][j];
            }
        }
        return result;
    }

    Matrix operator-(const Matrix &other) const {  // 矩阵相减
        if (rows != other.rows || cols != other.cols) {
            throw invalid_argument("Matrix sizes do not match.");
        }
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result.data[i][j] = data[i][j] - other.data[i][j];
            }
        }
        return result;
    }

    Matrix& operator++() {  // 矩阵自增
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                data[i][j]++;
            }
        }
        return *this;
    }

    Matrix operator++(int) {  // 矩阵后置自增
        Matrix result(*this);
        ++(*this);
        return result;
    }

    Matrix& operator--() {  // 矩阵自减
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                data[i][j]--;
            }
        }
        return *this;
    }

    Matrix operator--(int) {  // 矩阵后置自减
        Matrix result(*this);
        --(*this);
        return result;
    }

    bool operator==(const Matrix &other) const {  // 矩阵相等
        if (rows != other.rows || cols != other.cols) {
            return false;
        }
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                if (data[i][j] != other.data[i][j]) {
                    return false;
                }
            }
        }
        return true;
    }

    bool operator!=(const Matrix &other) const {  // 矩阵不等
        return !(*this == other);
    }

    friend ostream& operator<<(ostream &out, const Matrix &matrix) {  // 矩阵输出
        for (int i = 0; i < matrix.rows; i++) {
            for (int j = 0; j < matrix.cols; j++) {
                out << matrix.data[i][j] << " ";
            }
            out << endl;
        }
        return out;
    }

    friend istream& operator>>(istream &in, Matrix &matrix) {  // 矩阵输入
        for (int i = 0; i < matrix.rows; i++) {
            for (int j = 0; j < matrix.cols; j++) {
                in >> matrix.data[i][j];
            }
        }
        return in;
    }
};

使用示例：

int main() {
    Matrix a(2, 2), b(2, 2);
    cin >> a >> b;
    cout << a + b << endl;
    cout << a - b << endl;
    cout << ++a << endl;
    cout << b++ << endl;
    cout << (a == b) << endl;
    cout << (a != b) << endl;
    return 0;
}