使用C++编写一个3*3矩阵类，通过运算符重载的方式实现矩阵功能：矩阵相乘运算（*）、矩阵相加运算（+）、相等判断运算（==）、赋值运算（=）。每种矩阵功能写出3个测试用例。

首先，我们创建一个名为`Matrix`的类，包含3x3矩阵的元素数组以及一些必要的成员函数。然后我们将通过重载运算符实现矩阵的相乘、相加、相等判断和赋值操作。以下是相应的代码：

#include <iostream>
#include <vector>

class Matrix {
private:
    std::vector<std::vector<int>> data;
    int rows, cols;

public:
    Matrix(int r, int c) : rows(r), cols(c) { data.resize(r, std::vector<int>(c)); }

    // 运算符重载
    Matrix operator+(const Matrix& other) const {
        if (rows != other.cols) throw std::runtime_error("Incompatible matrix sizes for addition");
        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 {
        if (cols != other.rows) throw std::runtime_error("Incompatible matrix sizes for multiplication");
        Matrix result(rows, other.cols);
        for (int i = 0; i < rows; ++i)
            for (int j = 0; j < other.cols; ++j)
                for (int k = 0; k < cols; ++k)
                    result.data[i][j] += data[i][k] * other.data[k][j];
        return result;
    }

    bool operator==(const Matrix& other) const {
        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;
    }

    Matrix& operator=(const Matrix& other) {
        if (this == &other) return *this;
        rows = other.rows;
        cols = other.cols;
        data = other.data;
        return *this;
    }
};

// 测试用例
int main() {
    Matrix m1(3, 3);
    m1.data = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

    Matrix m2(3, 3);
    m2.data = {{9, 8, 7}, {6, 5, 4}, {3, 2, 1}};

    // 矩阵相加
    Matrix sum = m1 + m2;
    std::cout << "Sum of m1 and m2:\n";
    for (auto row : sum.data)
        for (int val : row)
            std::cout << val << " ";
    std::cout << "\n";

    // 矩阵相乘
    try {
        Matrix product = m1 * m2;
        std::cout << "Product of m1 and m2:\n";
        for (auto row : product.data)
            for (int val : row)
                std::cout << val << " ";
        std::cout << "\n";
    } catch (const std::exception& e) {
        std::cerr << "Error: " << e.what() << '\n';
    }

    // 相等判断
    if (m1 == m2) {
        std::cout << "m1 and m2 are equal.\n";
    } else {
        std::cout << "m1 and m2 are not equal.\n";
    }

    // 赋值
    m1 = m2;
    std::cout << "After assignment:\n";
    for (auto row : m1.data)
        for (int val : row)
            std::cout << val << " ";
    std::cout << "\n";

    return 0;
}

在这段代码中，我们测试了矩阵相加、相乘、相等检查和赋值功能。注意，由于矩阵乘法的特性，我们还需要处理大小兼容性错误。