Question

Is S a ring from the following multiplication and addition tables?

+ a b x a b

a a b a a a

b b a b a b

(a) Yes

(b) No

(c) Can’t Say

(d) Insufficient Data

The question was asked during an interview.

The origin of the question is Groups Rings and Fields topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Answer 1

Correct answer is (a) Yes

For explanation: S is a ring as it satisfies the properties G-i to R-iii.