用C++编写一个实现矩阵基础运算（加减乘除，求逆，转置等）的类的完整程序。

以下是一个简单的矩阵类的示例程序，包括基本矩阵运算（加减乘除，求逆，转置等）：

#include <iostream>
#include <vector>

using namespace std;

class Matrix {
public:
    Matrix(int row, int col) : m_row(row), m_col(col) {
        m_data.resize(row);
        for (int i = 0; i < row; ++i) {
            m_data[i].resize(col);
        }
    }

    int row() const { return m_row; }
    int col() const { return m_col; }

    double& operator()(int i, int j) { return m_data[i][j]; }
    double operator()(int i, int j) const { return m_data[i][j]; }

    Matrix operator+(const Matrix& other) const {
        Matrix res(m_row, m_col);
        for (int i = 0; i < m_row; ++i) {
            for (int j = 0; j < m_col; ++j) {
                res(i, j) = m_data[i][j] + other(i, j);
            }
        }
        return res;
    }

    Matrix operator-(const Matrix& other) const {
        Matrix res(m_row, m_col);
        for (int i = 0; i < m_row; ++i) {
            for (int j = 0; j < m_col; ++j) {
                res(i, j) = m_data[i][j] - other(i, j);
            }
        }
        return res;
    }

    Matrix operator*(const Matrix& other) const {
        Matrix res(m_row, other.m_col);
        for (int i = 0; i < m_row; ++i) {
            for (int j = 0; j < other.m_col; ++j) {
                for (int k = 0; k < m_col; ++k) {
                    res(i, j) += m_data[i][k] * other(k, j);
                }
            }
        }
        return res;
    }

    Matrix operator/(double scalar) const {
        Matrix res(m_row, m_col);
        for (int i = 0; i < m_row; ++i) {
            for (int j = 0; j < m_col; ++j) {
                res(i, j) = m_data[i][j] / scalar;
            }
        }
        return res;
    }

    Matrix transpose() const {
        Matrix res(m_col, m_row);
        for (int i = 0; i < m_row; ++i) {
            for (int j = 0; j < m_col; ++j) {
                res(j, i) = m_data[i][j];
            }
        }
        return res;
    }

    Matrix inverse() const {
        // TODO: implement matrix inverse
        return Matrix(m_row, m_col);
    }

private:
    int m_row;
    int m_col;
    vector<vector<double>> m_data;
};

int main() {
    Matrix A(2, 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;

    Matrix B(3, 2);
    B(0, 0) = 1; B(0, 1) = 2;
    B(1, 0) = 3; B(1, 1) = 4;
    B(2, 0) = 5; B(2, 1) = 6;

    Matrix C = A * B;
    Matrix D = C.transpose();

    cout << "A:" << endl;
    for (int i = 0; i < A.row(); ++i) {
        for (int j = 0; j < A.col(); ++j) {
            cout << A(i, j) << " ";
        }
        cout << endl;
    }

    cout << "B:" << endl;
    for (int i = 0; i < B.row(); ++i) {
        for (int j = 0; j < B.col(); ++j) {
            cout << B(i, j) << " ";
        }
        cout << endl;
    }

    cout << "C:" << endl;
    for (int i = 0; i < C.row(); ++i) {
        for (int j = 0; j < C.col(); ++j) {
            cout << C(i, j) << " ";
        }
        cout << endl;
    }

    cout << "D:" << endl;
    for (int i = 0; i < D.row(); ++i) {
        for (int j = 0; j < D.col(); ++j) {
            cout << D(i, j) << " ";
        }
        cout << endl;
    }

    return 0;
}

该程序中定义了一个Matrix类，可以表示一个矩阵。在构造函数中，使用vector实现了矩阵数据的存储，同时提供了访问矩阵元素的操作符()。并且实现了基本的矩阵加、减、乘、除、转置等运算，但是求逆运算需要自行实现。

在main函数中，创建了两个矩阵A和B，并对它们进行了乘法和转置运算，最后输出了它们的值。