Miscellaneous T...

G = {e, a, b, c} is an abelian group with e as identity element. The order of the other elements are

On the set of all natural numbers N, which one of the following * is a binary operation

If the binary operation * is defined on a set of ordered pairs of real numbers as (a, b), * (c, d) = (ad + bc, bd) and is associative, then (1, 2) * (3, 5) * (3, 4) =

A group (G,*) has 10 elements. The minimum number of elements of G, which are their own inverse is

Let G denote the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication

Z_n = {0, 1, 2,... (n – 1)} fails to be a group under multiplication modulo n because

The remainder obtained when 5¹²⁴ is divided by 124

The set of fourth roots of unity forms a group