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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