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Consider the binary operation * on Q defined by a * b = a + 12b + ab for a, b ∈ Q. Show that * is not commutative.

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1, 2 ∈ Q 

Now 1 * 2 = 1 + 12(B) + 1(B) = 27 and 2 * 1 = 2 + 12(A) + 2(A) = 16 

  1 * 2  2 * 1 

 * is not commutative. 

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