L-3 Set of all positive rational numbers under a*b=ab/3 form infinite abelian group Bsc math

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Show that set of all positive rational numbers forms abelian grp under operation * (a*b = ab /3) Show that set of all positive rational numbers forms abelian grp under operation * (a*b = ab /3)
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 the set of all Q+ under composition defined by a*b = ab/3 forms an infinite abelian group. Show that the set of all Q+ under composition defined by a*b = ab/3 forms an infinite abelian group.
Show that G = { a + √3b : a,b ∈ Q } is an abelian group under addition of real numbers. Show that G = { a + √3b : a,b ∈ Q } is an abelian group under addition of real numbers.
Show that set Q+ of all +ve rational numbers forms an abelian group under operation * (a*b = ab/2) Show that set Q+ of all +ve rational numbers forms an abelian group under operation * (a*b = ab/2)
11. If set of all positive rational numbers aob=ab/3 forms group; find identity, inverse of a. NEB12 11. If set of all positive rational numbers aob=ab/3 forms group; find identity, inverse of a. NEB12
Show that (𝑄^+, ∗) is a group, define as 𝑎∗𝑏=𝑎𝑏/3 Show that (𝑄^+, ∗) is a group, define as 𝑎∗𝑏=𝑎𝑏/3
Show that the set of all positive rational numbers forms an abelian Group under the composition Show that the set of all positive rational numbers forms an abelian Group under the composition