Класс matrix. Не получается перегрузить оператор =

#include <fstream>
#include "matrix.h"
using namespace std;
 
ofstream cout ("output.txt");
 
#define FOR(i,n)    for(int i=0; i<n; ++i)
 
class matrix {
    int size;
    double **mtr;
public:
    //конструкторы
    matrix (const int n = 3);
    matrix (const matrix&);
    double* &operator [] (int i) {return mtr[i];}
    int get_size () {return size;}
    
 
 
    //арифметические операции
    matrix& operator = (const matrix& a){
        if (this == &a)
            return (*this);
 
        size = a.size;
        FOR (i,size)
            FOR(j,size)
            mtr[i][j] = a.mtr[i][j];
 
    }
    friend const matrix operator + (matrix&, matrix&);
    friend const matrix operator - (matrix&, matrix&);
    friend const matrix operator * (matrix&, matrix&);
    friend const matrix operator - (matrix&);  // унарный минус
    friend matrix& operator += (matrix&, matrix&);
    friend matrix& operator -= (matrix&, matrix&);
    friend matrix& operator *= (matrix&, matrix&);
    friend bool operator == (matrix&, matrix&);
 
    friend ostream& operator << (ostream&, matrix&);
};
int main(){
    matrix a(3), b(3);
    a[0][0] = b[1][2] = 2;
    cout << a << endl << b;
    matrix c = a;  // не работает!!
    return 0;
}

matrix :: matrix (matrix& a){
    size = a.get_size();
    FOR (i,size)
        FOR (j,size)
            mtr[i][j] = a.mtr[i][j];
}

matrix :: matrix (matrix& a)
    :matrix(a.getsize())
{
    size = a.get_size();
    FOR (i,size)
        FOR (j,size)
            mtr[i][j] = a.mtr[i][j];
}

matrix :: matrix (matrix& a){
    size = a.get_size();
    try{
        mtr = new double*[size];
        FOR(i,size)
            mtr [i] = new double[size];
    }catch (bad_alloc)  {return;}
    FOR (i,size)
        FOR (j,size)
            mtr[i][j] = a.mtr[i][j];
}

matrix :: matrix (matrix& a) : matrix(a.get_size())