24 votes 24 votes 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: $3$ and $13$ $2$ and $11$ $4$ and $13$ $8$ and $14$ Set Theory & Algebra gatecse-2005 set-theory&algebra normal group-theory + – gatecse asked Sep 21, 2014 edited May 29, 2018 by Arjun gatecse 7.1k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 27 votes 27 votes Option C. Identity element here is $1.$ $4 * 4 \mod 15 = 1$ $7 * 13 \mod 15 = 1.$ anshu answered Feb 6, 2015 selected Feb 6, 2015 by Arjun anshu comment Share Follow See all 4 Comments See all 4 4 Comments reply Sachin Mittal 1 commented Jan 24, 2017 i edited by Puja Mishra Jan 20, 2018 reply Follow Share It is same as finding modular inverse, which is also last step in RSA. You may likely to know actual procedure for even big numbers- https://goo.gl/ZCza9r 21 votes 21 votes chinmoyghosh commented Jan 25, 2019 reply Follow Share How the identity element is 1? 0 votes 0 votes Meet2698 commented Jan 31, 2019 reply Follow Share An Identity element is an element which leaves other elements unchanged when combined with them. e.g a # e = a Here e is an identity element, # is any random operator. For multiplication,1 multiplying with any other number gives that number itself. e.g, 5 x 1 = 5 Hence 1 is an identity element with respect to multiplication. 0 votes 0 votes KUSHAGRA गुप्ता commented Jul 6, 2019 reply Follow Share $\\ 4d\equiv 1(mod15)\\ GCD(4,15)=1\ How?\\ 15=4*3+3\\ 4=3*1+\mathbf{1}\\ Now\ to\ find\ inverse\ of\ 4\ backtrack\ euclidean\ algorithm\\ 1=4-3*1\\ 1=4-1(15-4*3)\\ 1= 4.4-15.1\\ Taking\ (Mod 15) \ on\ both\ sides\\ 1mod(15)=4.4\\ Hence\ inverse\ of\ 4\ is\ 4$ 2 votes 2 votes Please log in or register to add a comment.
0 votes 0 votes 😊😊😊😊😊😊😊😊😊😊😊😊 akshay_123 answered Sep 14, 2023 akshay_123 comment Share Follow See all 0 reply Please log in or register to add a comment.
–3 votes –3 votes The correct answer is,(c) 4 and 13 Warrior answered Aug 20, 2017 Warrior comment Share Follow See all 2 Comments See all 2 2 Comments reply ankit3009 commented Oct 4, 2021 reply Follow Share The correct answer is 4 and 13 only, right? I drawn the cayley table and the result is 4 and 13. Please confirm. 0 votes 0 votes abir_banerjee commented Aug 9, 2022 reply Follow Share Yes you are right 0 votes 0 votes Please log in or register to add a comment.