I'm really confused on how to approach this question:
Recall that the Cartesian product $A \times A$ is defined as the set $\{(x, y) : x \in A \land y \in A \}$. 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 $A \ne \varnothing$ where the number $|A|$ of elements of $A$ is $20$ less than the number $|A\times A|$ of elements in $A\times A$. Thus $|A| + 20 = |A\times A|$. Determine the number of elements in $A$.
Thank you in advance!