Why operator= returns reference not const reference

Question

The original question is related to overloading operator= and I like to share my findings as it was nontrivial for me to find them. I cannot imagine reasonable example to us

Answer 1

I've spent some time and here is my example:

class A
{
public:
    const A& operator= (const A& a) {return *this;}
};

int main(int argc, char* argv[])
{
    A a1;
    A& a2 = a1;
    A& a3 = (a2 = a1);
}

and the compiler output: : error C2440: 'initializing' : cannot convert from 'const A' to 'A &'

I've checked it on MS VS 2010, but is it true on other platforms? And if this example is sufficient condition for = to be non const?