Why is my friend class declaration not working in C++?

Question

I am a beginner learning C++. While studying the topic of friends, I would like to try establishing a friend relationship between the class A in a.h and the class B in b.h, specifically for the get_value() member function. this is my code:

// a.h
#ifndef A_H
#define A_H
#include "b.h"

class A;

class A {
    friend void B::get_value(A&);
private:
    double m;
    int n;
public:
    A(double m = 100, int n = 200) : m(m), n(n) {}
};

#endif

// b.h
#ifndef B_H
#define B_H
class A; 

class B {
public:
    void get_value(A&);
};

#include "a.h"
#include <iostream>

void B::get_value(A& a) {
    std::cout << a.m << a.n << std::endl; 
    return;
}
#endif

// test.cpp
#include "a.h" 
#include "b.h" 

int main() {
    A a; 
    B b; 
    b.get_value(a); 
    return 0;
}

Writing it like this would result in an error, and the error message would be as follows:

E:/project/cpp_project/cpp_study/1. complex/b.h: In member function 'void B::get_value(A&)':
E:/project/cpp_project/cpp_study/1. complex/b.h:18:18: error: invalid use of incomplete type 'class A'
   18 |     std::cout << a.m << a.n << std::endl; 

I tried alternative approache: define B::get_value(A&) in a.h:

// a.h
#ifndef A_H
#define A_H
#include "b.h"

class A;

class A {
    friend void B::get_value(A&);
private:
    double m;
    int n;
public:
    A(double m = 100, int n = 200) : m(m), n(n) {}
};

#include <iostream>
void B::get_value(A& a) {
    std::cout << a.m << a.n << std::endl; // 访问A类的私有成员m和n
    return;
}

#endif

// b.h
#ifndef B_H
#define B_H
class A; // 前置声明A类

class B {
public:
    void get_value(A&);
};

#endif

It doesn't work but the error message has changed:

E:/project/cpp_project/cpp_study/1. complex/a.h:21: multiple definition of `B::get_value(A&)'; CMakeFiles/cpp_study.dir/1._complex/test.cpp.obj:E:/project/cpp_project/cpp_study/1. complex/a.h:21: first defined here
collect2.exe: error: ld returned 1 exit status
ninja: build stopped: subcommand failed.

Finally, I reached out to New Bing for help, and I received the answer. It move the definition of B::get_value() into b.cpp:

// a.h
#ifndef A_H
#define A_H
#include "b.h"

class A;

class A {
    friend void B::get_value(A&);
private:
    double m;
    int n;
public:
    A(double m = 100, int n = 200) : m(m), n(n) {}
};

#endif

// b.h
#ifndef B_H
#define B_H
class A; // 前置声明A类

class B {
public:
    void get_value(A&);
};

#endif

// b.cpp
#include "b.h" // 包含B类的定义
#include "a.h"
#include <iostream>

void B::get_value(A& a) {
    std::cout << a.m << a.n << std::endl; // 访问A类的私有成员m和n
    return;
}

It works but I don't understand. I hope someone can tell me why my code is error-prone and why bing's code is right.