The cartesian product $A \times A$ has $9$ elements among which are found $(- 1, 0)$ and $(0, 1)$ . Find the set $A$ and the remaining elements of $A \times A$ .

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Solution

$n (A \times A) = 9$
Set $A = {- 1, 0, 1}$ Since $(- 1, 0)$ and $(0, 1)$ are elements in $A \times A$
Remaining elements
$= {(- 1, - 1), (- 1, 1), (0, - 1), (0, 0), (1, - 1), (1, 0), (1, 1)}$

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A

A \times A

9

(- 1, 0)

(0, 1)

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