Which of the following are the subgroups? a) The set of all nxn matrices with determinant 2. b) The set of all upper triangular nxn matrices with no zeros on the diagonal. c) The set of all nxn matrices with determinant -1. d) All the above. Which one of the following is true? a) Every abelian group is cyclic. b) Every group of order 4 is cyclic. c) Every cyclic group of order > 2 has at least 2 distinct generators. d) None of the above The maximum order of an element in S is a) 100 b) 215 c) 115 d) 105 The order of the element (4,2) in ZxZgis a) 12 b) 20 c) 4 d) 2 The quotient and remainder obtained when f(x)=x+3x+4x²-3x+2 is divided by g(x)=x+2x-3 in Z[x]. a) q(x) = x²+x+x²+x and r(x)=4x+3 b) q(x)=x+x+x²-2 and r(x)=4x+3 c) q(x)=x+x+x²+x-2 and r(x)=4+3 ₫) q(x) = x² + x² + x²+x-2 andr(x)=4x+3