Question

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 $A\times A$.

Answer 1

Here $(-1,0)ϵA\times A\Rightarrow -1ϵA$ and $0ϵA$

$(0,1)ϵA\times A\Rightarrow 0ϵA$ and $1ϵA$

$\therefore$ $-1,0,1ϵA.$

It is given that $n(A\times A)=9$ which implies that n(A) = 3

$\therefore A=\{-1,0,1\}$

$\therefore A\times A=\left\{\right(-1,-1),(-1,0),(-1,1),$

$(0,-1),(0,0),(0,1),(1,-1),(1,0),(1,1)$

So the remaining elements of $A\times A$ are (-1, 1), (-1, 1), (0, -1), (0, 0), (1, -1), (1, 0) and (1, 1).