copy constructor issues with vector class

[bigc++]

Hey there. Newbie c++ student here. I am experiment with copy constructors and STL containers. I made a test class A and gave it an assignment operator and a copy constructor. I then instantiated an object of type A and then a vector to hold objects of this class A. Then I used push_back method to insert an instance of A and I get an error in Visual C++ 2010 that breaks to the push_back implementation in vector.cpp.

#include <iostream>
#include <vector>
using namespace std;



class A
{
public:
	A();
	A(int a, int b);
	~A();
	A(const A& src);
	A operator= (const A &rhs);
private:
	int a;
	int * b;
};

A::A()
{
	a = 0;
	b = nullptr;
	cout << endl << "A 0 argument constructor called";
}

A::A(int a, int b)
{
	this->a = a;
	this->b = new int;
	*this->b = b;
	cout << endl << "A 2 argument constructor called";
}

A::~A()
{
	a = 0;
	delete b;
	cout << endl << "A destructor called";
}


//There is a problem with this copy constructor
A::A(const A& src)
{
	this->a = src.a;
	this->b = new int;
	*this->b = *src.b;
	cout << endl << "A copy constructor called";
}


A A::operator= (const A &rhs)
{
	A tempA(rhs.a, *rhs.b);
	return tempA;
}




int main()
{
	A a1(1, 2);
	A a2;

	vector <A> v1;
	v1.push_back(a1);
	v1.push_back(a2);
	
	system("pause");
	return 0;
}

Object a1 adds just fine into the vector v1, but a2 does not. The problem seems to be with the fact that it was instantiated with my provided 0 argument constructor which assigns the pointer member to nullptr. Here is the output before the debugger breaks:

"
A 2 argument constructor called
A 0 argument constructor called
A copy constructor called
A copy constructor called
A destructor called
"


Now. when I change the default constructor A::A() to assign a memory using "new int" and assign a value to the int, then it adds just fine to the vector and the following output is produced:

"

A 2 argument constructor called
A 0 argument constructor called
A copy constructor called
A copy constructor called
A destructor called
A copy constructor called
"


Something is going on with the pointer in A::A() and I cannot figure out what it is after having read through some copy pointer tutorials. Your debugging help is appreciated. Knowing whats wrong will deeply improve my knowledge of C++