# Solution - Concept of Binary Operations

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#### Question

Show that the binary operation * on A = R – { – 1} defined as a*b = a + b + ab for all a, b ∈ A is commutative and associative on A. Also find the identity element of * in A and prove that every element of A is invertible.

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#### Similar questions

Let * be a binary operation, on the set of all non-zero real numbers, given by a** b = (ab)/5 for all a,b∈ R-{0} that 2*(x*5)=10

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Let A = Q ✕ Q, where Q is the set of all rational numbers, and * be a binary operation defined on A by (a, b) * (c, d) =  (ac, b + ad), for all (a, b) (c, d) ∈ A.
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(ii) the invertible element of A.

(iii)and hence write the inverse of elements (5, 3) and (1/2,4)

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LetA= R × R and * be a 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. Also find the inverse of every element (a, b) ε A.

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