GATE | GATE-CS-2004 | Question 72

The following is the incomplete operation table a 4-element group.

 *  e  a  b  c
 e  e  a  b  c
 a  a  b  c  e

The last row of the table is
(A) c a e b

(B) c b a e
(C) c b e a
(D) c e a b

Answer: (D)

Explanation: It is given that the given set of 4 elements is group.

The element ‘e’ is clearly identity as the row corresponding to it has all values same as the other operand. Also, since a*c is e, c*a should also be e which is only the case in option D

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