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Let A = N×N and ⋅ be the binary operatio...

Let A = N×N and ⋅ be the binary operation on A defined by(a, b) ⋅(c, d) = (a + c, b + d) . Show that ⋅ is commutative and associative. Find the identity element for ⋅ on A, if any.

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To solve the problem step by step, we will show that the binary operation defined on the set \( A = \mathbb{N} \times \mathbb{N} \) is commutative and associative, and then find the identity element if it exists. ### Step 1: Show that the operation is commutative. **Definition of Commutative Property:** A binary operation \( \cdot \) is commutative if for all \( (a, b), (c, d) \in A \): \[ (a, b) \cdot (c, d) = (c, d) \cdot (a, b) ...
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