Trying to understand "&&"

I thought I understood the "&&" until the following simple example did
not work.
Can someone tell me which is the problem or what I did not understand?

It add 2 strings and "cout" the result.

Special thanks for your time!

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g++ -std=c++0x main.cpp
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-- main.cpp ------
#include <iostream>
#include <cstring>
using namespace std;

class A
{
public:
    A() : str(0) { cout << "A()" << endl; }
    A(const char *string) : str(0) { str = new char[strlen(string) + 1];
strcpy(str, string); cout << "A(const char*)" << endl; }
    ~A() { delete[] str; cout << "~A()" << endl; }
    A(A &a) : str(0) { str = new char[strlen(a.str) + 1]; strcpy(str,
a.str); cout << "A(A&)" << endl; }
    A(A &&a) : str(0) { str = a.str; a.str = 0; cout << "A(A&&) : " << str
<< endl; }
    A &operator=(A &a) {
        delete[] str; str = 0;
        str = new char[strlen(a.str) + 1];
        strcpy(str, a.str);
        cout << "A = &A" << endl;
        return *this;
    }
    A &operator=(A &&a) {
        delete[] str;
        str = a.str; a.str = 0;
        cout << "A = &&A" << endl;
        return *this;
    }
    A &&operator+(A &a) {
        A b;
        b.str = new char[strlen(this->str) + strlen(a.str) + 1];
        strcpy(b.str, this->str);
        strcpy(b.str + strlen(this->str), a.str);
        cout << "A + A = " << b.str << endl;
        return std::move(b);
    }
    const char *operator*() { return str; }
protected:
    char *str;
};

int main()
{
    A a("Uni");
    A b("verse");
    A c = a + b;
    cout << *c << endl;
    cout << *(a+b) << endl;
    return 0;
}
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