In which of following stuctures is valid implication $x\cdot y=1\implies x=1$?
a) $(\mathbb{N}, *)$
b) $(\mathbb{Z}, *)$
c) $(\mathbb{Q}, *)$
d) $(\mathbb{C}, *)$
Solution is a), I can prove it by using simple example for all of four sets, but I need more general explanation.