2.1 Please provide detailed solution with explanation and justification asap to get a upvote for Each part PleaseFor all parts please 2.1 Is it a group?For every question write down if a group is Abelian.1. Does the (Z, +) (Integers under addition) form a group?2. Does the (Q, *) (Rational numbers under multiplication) form a group?3. Does the (Z11, '– mod 11') form a group?4. Does the (Z13, x mod 11) form a group?5. Does the (IR{0}, +) (Reals under division) form a group?6. Does the (C - {0}, +) Compler numbers under multiplication7. Does the (G, o) form a group? G = (f : ƒ is a bijection on S), o -composition of two functions, a set Sbijections of a set).{&, 0, A} (Hint: Set of all%3D8. Does a (G, x) form a group? G is a set of matrices of the size 2 x 2 ofinteger entries and nonzero determinant. x operation is a matrix multi-plication.

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Answered: 2.1 Is it a group? For every question…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 21E

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2.1 Is it a group? For every question write down if a group is Abelian. 1. Does the (Z, +) (Integers under addition) form a group? 2. Does the (Q, *) (Rational numbers under multiplication) form a group? 3. Does the (Z11, '- mod 11') form a group?