Answer
a) $A^2=\{(0,0), (0,1), (0,3), (1,0), (1,1), (1,3), (3,0), (3,1), (3,3)\}$
b) $A^2=\{(1,1),(1,2), (1,a), (1,b),(2,1),(2,2), (2,a), (2,b), (a,1),(a,2), (a,a), (a,b), (b,1),(b,2), (b,a), (b,b)\}$
Work Step by Step
We know $A^2=A \times A=\{(a,b): a\in A \text{ and } b\in A\}$. We will use this to do parts (a) and (b).
a) For $A=\{0,1,3\}$, $A^2=\{(0,0), (0,1), (0,3), (1,0), (1,1), (1,3), (3,0), (3,1), (3,3)\}.$
b) For $A=\{1,2,a,b\}$, $A^2=\{(1,1),(1,2), (1,a), (1,b),(2,1),(2,2), (2,a), (2,b), (a,1),(a,2), (a,a), (a,b), (b,1),(b,2), (b,a), (b,b)\}.$
