Abstract Algebra

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Direct Products & Operations: $\mathbb{R}^{\ast}\times\mathbb{R}$

ABSALG-HKREEQ

Which of the following operations make $\mathbb{R}^{\ast}\times \mathbb{R}$ into a group?

Select ALL that apply.

A

$(a,b)\star(c,d)=(ac,ad+b)$

B

$(a,b)\star(c,d)=(ac,d+b)$

C

$(a,b)\star(c,d)=(a+c,bd)$

D

$(a,b)\star(c,d)=(a+c,d+b)$

E

$(a,b)\star(c,d)=(ac^{-1},d+b)$