Overloading operators "=" and "+" do not work when combined in C++

#include <iostream>
using namespace std;
class A
{
public:
    A(int a)
    {
        length = a;
    }
    ~A(){}

    friend A operator +(A& var1, A& var2);
    A& operator=(A &other);

    int length;
};

A operator +(A& var1, A& var2)
{
    return A(var1.length + var2.length);
}

A& A::operator=(A &other)
{
    length = other.length;
    return *this;
}


int main()
{
    A a(1);
    A b(2);
    A c(3);
    c = a;   // work
    c = a + b;  // does not work
    cout << c.length ;
    return 0;
}

In main(), c = a is successfully compiled but "c = a + b" is not. However, in A& A::operator=(A &other), if I change (A &other) into (A other) then it works. Can anyone help me with this case?