Question

If $(A\times A)$ has 9 elements two of which are (-1,0) and (0,1), find the set A and the remaining elements of $(A\times A)$

Answer 1

Clearly, -1, 0 and 1 are elements of A.

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

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

$=\left\{\right(-1,-1),(-1,0),(-1,1),(0,-1),(0,0),(0,1),(1,-1),(1,0),(1,1\left)\right\}$

$\text{Hence, the remaining elements of A}\times \text{A are}$

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