Question

Let A={5,6}; how many binary operations can be defined on this set?

Answer 1

 = {5,6} has two elements e.g., 5 and 6 as you can see.
e.g., n(A) = 2 [ n(A) shows number of elements in set A } 
Then,  has 2 × 2 = 4 elements .
e.g., n(A × A) = 4 

we know, 
number of binary operation on set A=
= 2⁴ = 2 × 2 × 2 × 2 = 16 

Hence, number of binary operation on set A = 16 

Hope This helps :)