##### GATE 2005 -13 Group

The set {1,2,4,7,8,11,13,14} is a group under multiplication modulo 15 The inverses of 4 and 7 are respectively:

A.   3 and 13

B.   2 and 11

C.   4 and 13

D.   8 and 14

Solution:

Option C is correct.

The easy way to find the solution is :

Inverse for an element 'x' means an element 'y' such that when you perform the given operation between 'x' and 'y' the result should be identity element.

So for moudulo, the identity element is 1.

The inverse of 4 is:  ,so from given option y =4 as :

The inverse of 7 is:  , so from given option y=13 as: