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Let A=Q x Q and let * be a binary operat...

Let `A=Q x Q` and let * be a binary operation on A defined by `(a , b)*(c , d)=(a c , b+a d)` for `(a , b),(c , d) in Adot` Then, with respect to * on A Find the identity element in A Find the invertible elements of A.

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To solve the problem, we need to find the identity element and the invertible elements with respect to the binary operation defined on \( A = \mathbb{Q} \times \mathbb{Q} \). ### Step 1: Identify the Binary Operation The binary operation \( * \) is defined as: \[ (a, b) * (c, d) = (a \cdot c, b + a \cdot d) \] for \( (a, b), (c, d) \in A \). ...
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Let A=QxxQ and let ** be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b+a d) for (a ,\ b),\ (c ,\ d) in A . Then, with respect to ** on A . Find the identity element in A .

Let A=QxxQ and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b+a d) for (a ,\ b),\ (c ,\ d) in A . Then, with respect to * on Adot Find the invertible elements of A .

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Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a+c ,\ b+d) for all (a ,\ b),\ (c ,\ d) in Adot Show that * is associative on Adot

Let A = N xx N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Show that * is commutative.

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Let R_0 denote the set of all non-zero real numbers and let A=R_0xxR_0 . If * is a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b d) for all (a ,\ b),\ (c ,\ d) in Adot Show that * is both commutative and associative on A (ii) Find the identity element in A

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Let A = Q xxQ and ** be a binary operation on A defined by (a, b) ** (c,d) = (ad + b, ac). Prove that ** is closed on A = QxxQ . Find (i) Identity element of (A, **) , (ii) The invertible element of (A,**).

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
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