Problem 1. In each of the following, either prove or disprove that the given pair (G,) is a group. 1.1. G = R with binary operation ⚫ defined by ab=a+b+ab Va, bЄ R. 1.2. G is the space of matrices G = {A Є M2(Z) : det(A) = 0} with operation ● given by matrix multiplication. 1.3. G is the set of matrices G= {A Є M2(Z20) : det(A) = 1} with operation ⚫ given by matrix multiplication. Here Zo denotes the set of all non-negative integers.

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A: As per the guidelines we can answer the first question since u have posted multiple questions.

Q: 4. (i) Write the following permutations in S9 as a product of disjoint cycles 6 1 2 3 4 5 6 7 8 9 7…

A: Note: As per our guidelines, we will solve first three sub-parts. Please repost remaining parts.

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