The following table represents a set of rotational symmetries of anequilateral triangle where & is a rotation of 0 degrees around a centreof an equilateral triangle0 is a rotation of 120 degrees around the centreAnd A is a rotation of 240 degrees around the centre.The operator for the rotations is given as O.[The rotation symbols in the table can be found if you click oninsert and then click on the 2 symbol on the top right hand side ofyour computer screen.]4.1 Write down the identity element of the set and substantiate.4.2 Write down the set of inverse pairs4.3 Show that the associativity property is satisfied by the set4.4 Show that the group is commutative||

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 32E: Find the centralizer for each element a in each of the following groups. The quaternion group G={...

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4.1 Write down the identity element of the set and substantiate. 4.2 Write down the set of inverse pairs 4.3 Show that the associativity property is satisfied by the set