为什么我使用运算符*失败了?

我昨天早些时候问了一个问题，肯定得到了一些很好的答案。现在我的项目快结束了，我又卡住了，想不出答案。我将把我的代码中最相关的部分放在这里，希望能从你们那里得到一些见解。要求是:我不能更改main.cpp中的代码，并且我的头文件应该尽可能简单。

#ifndef MATRIX_H
#define MATRIX_H
#include <vector>
#include <iostream>
#include <math.h>
#include <complex>
using namespace std;
namespace theMatrix {
template <typename T, size_t ROWS, size_t COLS>
class Matrix {
    friend class Matrix;
public:
    Matrix(const T & init = T()) : elts(ROWS, vector<T>(COLS, init)) {
    };
    const vector<T> & operator[](int ROWS) const {
        return elts[ROWS];
    };
    vector<T> & operator[](int ROWS) {
        return elts[ROWS];
    };
    //matrixMult
    template<size_t INNER>
    Matrix & matrixMult(const Matrix<T, ROWS, INNER> & mat1, const Matrix<T, INNER, COLS> & mat2) {
        for (int i = 0; i < ROWS; i++) {
            for (int j = 0; j < COLS; j++) {
                //elts[i][j] = 0;
                for (int k = 0; k < INNER; k++) {
                    this->elts[i][j] += mat1.elts[i][k] * mat2.elts[k][j];
                }
            }
        }
        return *this;
    };
    //print function
    void print(ostream & out) const {
        for (int i = 0; i < ROWS; i++) {
            for (int j = 0; j < COLS; j++) {
                out << elts[i][j];
            }
            out << "n";
        }
    };
private:
    vector< vector<T> > elts;
};
//Operator<<
template <typename T, size_t ROWS, size_t COLS>
ostream & operator<<(ostream & out, const Matrix<T, ROWS, COLS> & elts) {
    elts.print(out);
    return out;
};

//Operator*
template <typename T, size_t ROWS, size_t COLS>
Matrix<T, ROWS, COLS> operator*(const Matrix<T, ROWS, COLS> & lhs, const Matrix<T, ROWS, COLS> & rhs) {
    Matrix<T, ROWS, COLS> returnVal;
    return returnVal.matrixMult(lhs, rhs);
};
//operator matrixMult
template <typename T, size_t ROWS, size_t INNER, size_t COLS>
inline void matrixMult(const Matrix<T, ROWS, INNER> & mat1, const Matrix<T, INNER, COLS> & mat2, Matrix<T, ROWS, COLS> & mat3) {
    mat3 = matrixMult(mat1, mat2);
};

This is my main.cpp:

#include <iostream>
#include <fstream>
#include <string>
#include <cstdlib>  // for rand()
#include "Matrix.h"
using namespace std;
using namespace theMatrix;
template <typename T, size_t ROWS, size_t COLS>
void randomize(Matrix<T, ROWS, COLS> & mat)
// Put random values in a Matrix.
// Note:  It must be possible to assign T an int value.
{
for (size_t i = 0; i < ROWS; i++)
    for (size_t j = 0; j < COLS; j++)
        mat[i][j] = (rand() % 21) - 10; // Random number in range -10,...,+10
}
struct Complex
{
Complex(double re = 0.0, double im = 0.0) : real(re), imag(im) { }
Complex & operator+=(const Complex & rhs)
{
    real += rhs.real;
    imag += rhs.imag;
    return *this;
}
Complex & operator-=(const Complex & rhs)
{
    real -= rhs.real;
    imag -= rhs.imag;
    return *this;
}
Complex & operator*=(const Complex & rhs)
{
    real = real * rhs.real - imag * rhs.imag;
    imag = real * rhs.imag + imag * rhs.real;
    return *this;
}
double real;
double imag;
};
Complex operator+(const Complex & lhs, const Complex & rhs)
{
return Complex(lhs.real + rhs.real, lhs.imag + rhs.imag);
}
Complex operator-(const Complex & lhs, const Complex & rhs)
{
return Complex(lhs.real - rhs.real, lhs.imag - rhs.imag);
}
Complex operator*(const Complex & lhs, const Complex & rhs)
{
return Complex(lhs.real * rhs.real - lhs.imag * rhs.imag, lhs.real * rhs.imag + lhs.imag * rhs.real);
}
ostream & operator<<(ostream & out, const Complex & c)
{
out << "(" << c.real << " + " << c.imag << "i)";
return out;
}
int main()
{
// Matrix multiplication tests:
Matrix<int, 2, 3> m4;
randomize(m4);
Matrix<int, 3, 5> m5;
randomize(m5);
Matrix<int, 2, 5> m6;
Matrix<int, 2, 5> m7;
matrixMult(m4, m5, m7);
out << "m6 == m4 * m5: " << (m6 == m4 * m5) << endl; // here is the first error
// Matrices of Complex:
Matrix<Complex, 2, 8> m11;
randomize(m11);
Complex c(1, -3);
Matrix<Complex, 8, 3> m12;
randomize(m12);
out << "m11 * m12: " << endl << m11 * m12 << endl; // Here is the second error
out.close();
}

我只有两个错误，这与复杂的操作符*声明相冲突，我一直试图解决几个小时，我只是不能弄清楚。下面是错误:

Error        1        error C2678: binary '*' : no operator found which takes a left-hand operand of type 'nkumath::Matrix<T,ROWS,COLS>' (or there is no acceptable conversion) 
Error        2        error C2678: binary '*' : no operator found which takes a left-hand operand of type 'nkumath::Matrix<T,ROWS,COLS>' (or there is no acceptable conversion)               

再次感谢大家的帮助。

编辑:这是解决方案!我投了赞成票谢谢! !

//Operator*
template <typename T, size_t ROWS, size_t INNER, size_t COLS>
Matrix<T, ROWS, COLS> operator*(const Matrix<T, ROWS, INNER> & lhs, const Matrix<T, INNER, COLS> & rhs) {
    Matrix<T, ROWS, COLS> returnVal;
    return returnVal.matrixMult(lhs, rhs);
};