Question

Let $A$ be a non-empty set such that $A\times A$ has $9$ elements and $(-1,0),(0,1)$ are elements of $A\times A$, then $A=$

• A. $\{-1,0,2\}$
• B. $\{-1,0,1\}$
• C. $\{-2,0,1\}$
• D. Cannot be determined

Answer 1

The correct option is B $\{-1,0,1\}$

Given that $(-1,0)\in A\times A$ and
$(0,1)\in A\times A$
$\Rightarrow -1,0,1$ are elements of set $A$
and given that $n(A\times A)=9\Rightarrow n\left(A\right)=3$
$\therefore A=\{-1,0,1\}$