Question

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

Answer 1

A = { 5,6}
it is clear that number of elements in set A = 2
e.g., n (A) = 2

now, number of elements in set A × A = 2 × 2 = 4, e.g., n(A × A ) = 4

As you know,
$\text{number of binary operation on A }=\bold{n(A)^{n(A\times A)}}$
so, number of binary operation on A = 2⁴ = 16

Answer 2

16 I think is the answer