How do I calculate $(A\times B)^2$ for $A=\{1,2\}$ and $B=\{a,b,c\}$? 
Let $A = \{1,2\}$ and $B = \{a,b,c\}$, find $(A \times B)^2$.  

I found $(A \times B) = \{(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)\}$ 
But how do I find 
$$\{(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)\} \times \{(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)\} $$
?
Is it $\{(1,a,1,a),(1,a,1,b),(1,a,1,c), \ldots\}$ ?  
If I am wrong please show me the correct method. 
 A: You are wrong. 
The set 
$M:=\{(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)\} \times  \{(1,a),(1,b),(1,c),(2,a),(2,b), (2,c)\}$ 
consists of pairs of pairs.
For example $((1,a), (2,b)) \in M$.
A: You will get $36$ elements $$\{((1,a),(1,a)), ((1,a),(1,b)),...,  ((2,c),(2,c))\}$$ 
A: For completeness sake, the result is :
$\{\\
 ((1, a), (1, a)),
 ((1, a), (1, b)),
 ((1, a), (1, c)),
 ((1, a), (2, a)),
 ((1, a), (2, b)),
 ((1, a), (2, c)),\\
 ((1, b), (1, a)),
 ((1, b), (1, b)),
 ((1, b), (1, c)),
 ((1, b), (2, a)),
 ((1, b), (2, b)),
 ((1, b), (2, c)),\\
 ((1, c), (1, a)),
 ((1, c), (1, b)),
 ((1, c), (1, c)),
 ((1, c), (2, a)),
 ((1, c), (2, b)),
 ((1, c), (2, c)),\\
 ((2, a), (1, a)),
 ((2, a), (1, b)),
 ((2, a), (1, c)),
 ((2, a), (2, a)),
 ((2, a), (2, b)),
 ((2, a), (2, c)),\\
 ((2, b), (1, a)),
 ((2, b), (1, b)),
 ((2, b), (1, c)),
 ((2, b), (2, a)),
 ((2, b), (2, b)),
 ((2, b), (2, c)),\\
 ((2, c), (1, a)),
 ((2, c), (1, b)),
 ((2, c), (1, c)),
 ((2, c), (2, a)),
 ((2, c), (2, b)),
 ((2, c), (2, c))\\
\}$
