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