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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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Given `A:N×N` with binary operation * definrd by `(a,b)∗(c,d)=(a+c,c+d).`
Step:1-Checking if the operation is commutative:
An opertion ∗ on A is commutative if
`a∗b=b∗a∀a,bϵA`
...
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