Let * be a binary operation on R defined by a * b = ab + 1. Then, * is

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Show that the binary operation * on R defined by a*b=a + b + ab for all a, b ⋳ R is commutative as w Show that the binary operation * on R defined by a*b=a + b + ab for all a, b ⋳ R is commutative as w
Show that G=R-1 is an abelian group under the binary operation 𝑎∗𝑏=𝑎+𝑏−𝑎𝑏, ∀ 𝑎,𝑏∈𝐺. Show that G=R-1 is an abelian group under the binary operation 𝑎∗𝑏=𝑎+𝑏−𝑎𝑏, ∀ 𝑎,𝑏∈𝐺.
Let `A=Q x Q` and let * be a binary operation on A defined by `(a , b)*(c , d)=(a c , b+a d)` fo... Let `A=Q x Q` and let * be a binary operation on A defined by `(a , b)*(c , d)=(a c , b+a d)` fo...
Does the set R\{0} under the binary operation a*b = |ab| form a group? Does the set R\{0} under the binary operation a*b = |ab| form a group?
a binary operation * is defined by a*b =a+b+5 find the inverse element a binary operation * is defined by a*b =a+b+5 find the inverse element
Let A=RXR and * be a binary operation on A defined by (a,b)*(c,d) =(a+c,b+d). Prove that is commutat Let A=RXR and * be a binary operation on A defined by (a,b)*(c,d) =(a+c,b+d). Prove that is commutat
Show that * on R defined by a*b=ab^2 is a binary operation. Show that * on R defined by a*b=ab^2 is a binary operation.
Let * be a binary operation defined on Q+ by the rule a∗b=ab/3 for all a,b∈Q^+. The inverse of 4∗6 Let * be a binary operation defined on Q+ by the rule a∗b=ab/3 for all a,b∈Q^+. The inverse of 4∗6