GATE | GATE-CS-2006 | Question 3

The set {1, 2, 3, 5, 7, 8, 9} under multiplication modulo 10 is not a group. Given below are four plausible reasons. Which one of them is false?
(A) It is not closed
(B) 2 does not have an inverse
(C) 3 does not have an inverse
(D) 8 does not have an inverse


Answer: (C)

Explanation: A is not closed under multiplication as we may get 0 after multiplication and 0 is not present in set.

2 doesn’t have an inverse as there is no x such that (2*x) mod 10 is 1.

3 has an inverse as (3*7) mod 10 is 1.

8 doesn’t have an inverse as there is no x such that (2*x) mod 10 is 1.

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