Problème pointeurs tableau multi c++!

#include <iostream>
using namespace std;


int main(int argc, char* argv[])
{ 
		int **matrice = new int*[5];
	int k=0;
	for(unsigned int i=0;i<5;i++)
	{
		*matrice = new int[5];
		for(unsigned int j=0;j<5;j++)
		{
			**matrice = k;
			cout << **matrice;//voilà ce qui change!
			cout << "  ";
			*matrice++;//on fait pointer le pointeur sur l'entier suivant
			k++;
		}
		matrice++;//on fait pointer le pointeur sur le pointeur d'entier suivant 
		cout << "\n";

	}
}

//---- matrix_2d.hpp-----
#include <cassert>
#include <iostream>

template <typename Tdata>
class matrix_2d{
    protected:
        unsigned nb_row;
        unsigned nb_column;
        Tdata **data;
    public:

        matrix_2d(unsigned nb_row0,unsigned nb_column0):
            nb_row(nb_row0),
            nb_column(nb_column0)
        {
            data = new Tdata*[nb_row];
            for(unsigned i=0;i<nb_row;++i) data[i] = new Tdata[nb_column];
        }

        inline unsigned get_nb_row() const{
            return nb_row;
        }

        inline unsigned get_nb_column() const{
            return nb_column;
        }

        inline const Tdata & get(unsigned row,unsigned col) const{
            assert(row < nb_row);
            assert(col < nb_column);
            return data[row][col];
        }

        inline void set(unsigned row,unsigned col,const Tdata & val){
            assert(row < nb_row);
            assert(col < nb_column);
             data[row][col] = val;
        }
};

template <typename Tdata>
std::ostream & operator << (std::ostream & out,const matrix_2d<Tdata> & m){
    unsigned nb_row = m.get_nb_row(),nb_col = m.get_nb_column();
    for(unsigned i=0;i<nb_row;++i){
        for(unsigned j=0;j<nb_col;++j){
            out << m.get(i,j) << '\t';
        }
        out << std::endl;
    }
    return out;
}

//---- matrix_2d.hpp-----

//---- main.cpp ---------
// #include "matrix_2d.hpp"
// #include <iostream>

int main(){
    std::cout << "Création de m:" << std::endl;
    matrix_2d<int> m(5,3);
    std::cout << m;
    std::cout << "Initialisation de m:" << std::endl;
    unsigned nb_row = m.get_nb_row(),nb_col = m.get_nb_column(),k=0;
    for(unsigned i=0;i<nb_row;++i){
        for(unsigned j=0;j<nb_col;++j){
            m.set(i,j,k++);
        }
    }
    std::cout << m;
    return 0;
}

Création de m:
0       0       0
0       0       0
0       0       0
0       0       0
0       0       0
Initialisation de m:
0       1       2
3       4       5
6       7       8
9       10      11
12      13      14

using namespace std;

std::cout << matrice << ' ' << 6 << "plop" << std::endl;

(((((std::cout << matrice) << ' ') << 6) << "plop") << std::endl);