The following is the incomplete operation table of a 4-element group. * | e a b c e | e a b c a | a e c b b | b c e a c | ? ? ? ? The last row of the table is A. c a e b B. c b a e C. b c e a D. c r a b

GATE 2004 · Discrete Mathematics · Group Theory · medium

Answer: D. c, b, a, e

1. Apply Latin square constraint column by column: Column e contains {e, a, b, ?}; missing is c, so c*e = c. Column a contains {a, e, c, ?}; missing is b, so c*a = b. Column b contains {b, c, e, ?}; missing is a, so c*b = a. Column c contains {c, b, a, ?}; missing is e, so c*c = e.
2. Write the last row: Last row (c): c*e=c, c*a=b, c*b=a, c*c=e. So the row is c, b, a, e.