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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

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.

Find

(i) the identity element in A

(ii) the invertible element of A.

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

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.