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.

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