Question

If (G,•) is a group, then f:G×G→G, defined by f(g,h) =g², is a binary operation? Is it true?

Answer 1

Since (G,*) is a group then it satisfies the closure property: for every a, b in (G,*)

$a * b$ is present in (G,*)

Therefore $a^2$ is always present in (G,*) for every element a in (G,*), this implies that $f:G*G-G$ is a mapping from $G*G$ to $G$ , hence a binary operation