Template Type Matrix Class Addition: error in Proper Addition

Can anyone help me out finding why the sum of my matrices is not how they should be?

template <typename T>
Matrix<T> Matrix<T>::operator + (const Matrix<T> &M){
    Matrix<T> tmp(m,n,M.x); 
    for(int i=0;i<m;i++)
        for(int j=0;j<n;j++)
            tmp.Mat[i][j]+= Mat[i][j]+ M.Mat[i][j];
    return tmp; 
}

This is my program's body:

#include <iostream>
#include <vector>

template <typename T>
class Matrix {
private:
    unsigned int m; unsigned int n;
    std::vector<T> x;
    std::vector<T> y;
    std::vector<std::vector<int>> Mat;


public:
    Matrix (unsigned int m, unsigned int n, std::vector<T> x);
    Matrix (const Matrix<T> &M); //= default;
   // Matrix ();
    Matrix<T> operator = (const Matrix<T> &M);      // Assignment
    Matrix<T> operator + (const Matrix<T> &M);      // Addition
    Matrix<T> operator - (const Matrix<T> &M);      // Subtraction
    Matrix<T> operator * (const T &scalar);          // Scalar Multiplication
    Matrix<T> operator * (const Matrix<T> &M);      // Matrix Multiplication

    friend std::ostream& operator << (std::ostream& os, const Matrix<T> &M){

    for (int i = 0; i< M.m; i++){
        for (int j = 0; j< M.n; j++){
            os << M.Mat[i][j] << ' ';
        }
        os << '\n';
    }
    os << '\n' ;
    return os;
    }
};

template <typename T>
Matrix<T>::Matrix (unsigned int m, unsigned int n, std::vector<T> x){ //constructor
this -> m = m;
this -> n = n;
this -> x = x;

int index = 0;
Mat.resize(m);
for (unsigned int i = 0; i < Mat.size(); i++) {
    Mat[i].resize(n);
}
for (unsigned int i = 0; i<m; i++){
    for (unsigned int j = 0; j<n; j++){
        Mat[i][j] = x[index];
        index++;
    }
}
}

template<typename T>
Matrix<T>::Matrix(const Matrix &M) //copy constructor
:
m(M.m),
n(M.n),
Mat(M.Mat)
{}

And this is my main: Note: We were required in the initialization that the constructor should take in 2 unsigned integers and a linear container where the elements will be divided to rows and columns according to the inputted.

int main(){
std::vector<int> x = {1,2,3,4};
std::vector<int> y = {5,6,7,8};
std::vector<int> z = {9,10,11,12};

Matrix<int> A{2,2,x};
Matrix<int> B{2,2,y};
Matrix<int> C{2,2,z};

C = B;


std::cout << "A\n" << A;
std::cout << "B\n" << B;
std::cout << "C\n" << C;

Matrix<int> E(A + B);
std::cout << "E\n" << E;
}

When I add A and B I always get 11 14 17 20

It's like the matrix B doubles before adding to A

Thanks in advance!