Integers/Difference/Structural properties/Exercise

Consider the integers ${}\mathbb {Z}$ together with the difference as a binary operation, that is, the mapping

$\mathbb {Z} \times \mathbb {Z} \longrightarrow \mathbb {Z} ,(a,b)\longmapsto a-b.$

Does there exist a neutral element for this operation? Is this operation associative, commutative, does there exist for every element an inverse element?

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