If A = {–1, 1}, find A × A × A.
Question:

If $A=\{-1,1\}$, find $A \times A \times A$.

Solution:

It is known that for any non-empty set A, A × A × A is defined as

$\mathrm{A} \times \mathrm{A} \times \mathrm{A}=\{(\mathrm{a}, b, c): a, b, c \in \mathrm{A}\}$

It is given that $A=\{-1,1\}$

$\therefore A \times A \times A=\{(-1,-1,-1),(-1,-1,1),(-1,1,-1),(-1,1,1)$

$(1,-1,-1),(1,-1,1),(1,1,-1),(1,1,1)\}$

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