C++ :: Defining Operator In Abstract Class

I have an abstract class called Mbase and from it derived two classes: Sparse and Dense. Now I have an array in which its elements can be either Sparse or Dense. So, I delcared the array to have pointers to Mbase class. For example:

PHP Code:
Mbase** A;
Sparse* A1 = new Sparse;
Dense* A2 = new Dense;
A[1] = dynamic_cast<Mbase*>(A1);
A[2] = dynamic_cast<Mbase*>(A2); 

Now, I have operator + defined in Sparse and Dense. but when I do

PHP Code:

A[1]+A[2] 

I get that operator + is not defined for Mbase class. So, I tried to define it in the Mbase class

PHP Code:

class Mbase{
public:
void put()=0;
double get()=0;
Mbase operator +(Mbase A);
} 

However, the last code does not compile complaining that it cannot declare a class of type abstract in Mbase operator +(Mbase A). I think this is because I am returning Mbase instance.