Prove Q⁺ is an Abelian Group Under the Operation a ∘ b = (ab)/2 | Abstract Algebra Explained

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Show that the set of Q+ forms an abelian group under the operation defined by a * b = ab/2 Show that the set of Q+ forms an abelian group under the operation defined by a * b = ab/2
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.
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