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Question

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


A
A={1,0}
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B
A={0,1}
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C
A={1,0,1}
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D
A={1,1}
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Solution

The correct option is A $$A=\left\{ -1,0,1 \right\}$$
Given $$A\times A$$ has $$9$$ elements $$\Rightarrow n(A)=3$$
Elements of $$A\times A  $$ are  $$(-1,0)$$  &  $$(0,1)$$.
$$\therefore$$ $$A$$ needs to contain $$-1, 0$$ and $$1$$.
$$\therefore$$ Since $$n(A)=3 \Rightarrow  A=\left \{ -1,0,1 \right \}$$

Mathematics

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