Let S = {a,b} and define two operations ⊕ and ⊗ on S by the following charts:(a) Verify th...

Let S = {a,b} and define two operations ⊕ and ⊗ on S by the following charts:

(a) Verify that S together with ⊕ and ⊗ satisfies the axioms of a field.

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(b) Identify the elements of S that are “0,” “1”  and “-1.”