Cartesian Product for sets Recall that the Cartesian product $A\times A$ is defined as the set $\{(x,y) : x ∈ A \land y ∈ A\}$ . Thus if for
example $A = \{1,2,3\}, A\times A = \{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)\}$.
Consider a set $A$ is not empty where the number $|A|$ of elements of $A$ is 20 less than the number $|A\times A|$ elements in $A\times A$. Thus $|A| + 20 = |A\times A|$. Determine the number of elements in $A$.
My attempt: I thought from set $A$ there are only 3 elements, $\{1,2,3\}$? but and 9 elements in set $A\times A$ but then the math does not work because 3 + 20 does not equal 9.
Could someone help me please?
Thanks

$x+20=x^2$ and so $x^2-x=20$ or $x(x-1)=20$ so $x=5$. I mean $|A|=5$.
