Matrix C++ problem with overloading operators - c++

Question

I'm making simple matrix calculator for school project. I tried to use overloading operators but I have problem with operator "=". I checked it in debugger in Visual Studio and after assigning data from matrix A to matrix X all of data disappears. How should I repair this? Thank you in advance for your help and advice.
#include <iostream>
#include <vector>
#include <conio.h>
#include <stdlib.h>
using std::vector;
class Matrix {
private:
int rows, cols;
vector<vector<double>> matrix;
public:
Matrix(int r = 0, int c = 0) : rows(r), cols(c) {
std::vector<std::vector<double>> M(rows, std::vector<double>(cols));
matrix = M;
}
~Matrix() {}
// void operator+(const Matrix &rhs);
double get_rows() { return rows; }
double get_cols() { return cols; }
void set_matrix_value() {
std::cout << "Put values in your matrix\n";
for(int i = 0; i < matrix.size(); i++) {
for(int j = 0; j < matrix[i].size(); j++) {
// this->matrix[i][j] = int(_getch() - '0');
std::cin >> matrix[i][j];
}
}
}
void display_matrix() {
for(int i = 0; i < matrix.size(); i++) {
std::cout << "|";
for(int j = 0; j < matrix[i].size(); j++) {
std::cout << matrix[i][j];
if(j != matrix[i].size() - 1) {
std::cout << " ";
}
}
std::cout << "|\n";
}
}
Matrix operator=(const Matrix& M) {
rows = M.rows;
cols = M.cols;
Matrix new_matrix(rows, cols);
std::vector<std::vector<double>> m(rows, std::vector<double>(cols));
new_matrix.matrix = m;
for(int i = 0; i < m.size(); i++) {
for(int j = 0; j < m[i].size(); j++) {
new_matrix.matrix[i][j] = M.matrix[i][j];
}
}
return new_matrix;
}
Matrix operator+(const Matrix& m) {
if(rows != m.rows && cols != m.cols) {
std::cout << "Matrix sizes do not match. Write martix again.";
return (*this);
}
Matrix new_matrix(rows, cols);
for(int i = 0; i < rows; i++) {
for(int j = 0; j < cols; j++) {
new_matrix.matrix[i][j] = matrix[i][j] + m.matrix[i][j];
}
}
return new_matrix;
}
};
int main() {
// int k;
// int rows, cols;
Matrix X;
// std::cout << "Welcome in Matrix Mode!\n";
X.display_matrix();
Matrix A(3, 3);
A.set_matrix_value();
A.display_matrix();
X = A;
std::cout << X.get_rows() << " " << X.get_cols();
X.display_matrix();
}