Short Answer TypeState whether the following statements are true or false. Justify.
(i) For an arbitrary binary operation * on a set N, a*a = a ∀ a ∈N.
(ii) If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a.
Consider a binary operation * on N defined as a * b = a3Â + b3Â . Choose the correct answer.
(A) Â Â Â Is * both associative and commutative ?
(B) Â Â Â Is * commutative but not associative?
(C) Â Â Â Is * associative but not commutative?
(D) Â Â Â Is * neither commutative nor associative?
Let A = Q x Q. Let be a binary operation on A defined by (a, b) * (c, d) = (ac, ad + b).
Then
(i) Find the identify element of (A, *)
(ii) Find the invertible elements of (A, *)
Define binary operation ‘*’ on Q as follows : a * b = a + b – ab, a, b∈ Q
(i) Find the identity element of (Q, *).
(ii) Which elements in (Q. *) are invertible?
 is the inverse of a ≠0 for the multiplication operation ‘x’ on R.
As a + (– a) = a – a = 0 and (– a) + a = 0, – a is the inverse of a for addition.
Similarly, for
 is the inverse of a for multiplication.
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