Do I have to return a reference to the object when overloading a pre-increment operator?

Can I use:

MyClass& MyClass::operator++ () {
    a++;  // private var of MyClass
    return (*this);
}

Or it can be:

MyClass MyClass::operator++ ();

What's the difference?

Thanks for answers. I have another issue.

Many people do something like that:

MyClass& MyClass::operator++();
MyClass MyClass::operator++(int);

Isn't it illogical? Please give some examples if you can.

I know that the first version is pre-increment and the second is post-increment, but i ask why the first one returns reference but the second one not? It is in the same code (class), and the same use of the code.