Let's Do Some Abstract algebra!

Algebra Level 4

Consider the set of integers $$\mathbb Z$$ with an operation $$*$$ defined by, $$a * b = a^b$$ for all $$a, b \in \mathbb Z$$ then consider the following statements:

(1): $$\mathbb Z$$ with operation $$*$$ is groupoid.
(2): $$\mathbb Z$$ with an operation $$*$$ is group.
(3): $$\mathbb Z$$ with an operation $$*$$ is not a group.

×