with the following multiplication table: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Question

with the following multiplication table: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2 1 6 78 345 12 13 14 9 10 11 16 15 3 12 4 9 10 2 6 16 1 11 15 7 8 13 5 14 4 7 9 1 11 12 2 14 3 15 5 6 16 8 10 13 5 8 10 11 1 13 14 2 15 3 4 16 6 7 9 12 6 9 7 12 13 1 3 15 2 14 16 4 5 10 8 11 74 12 2 14 9 1 11 6 16 8 3 15 5 13 10 8 5 13 14 2 10 11 1 16 6 7 15 3 4 12 9 9 6 1 3 15 7 12 13 4 5 10 2 14 16 11 8 10 16 11 15 3 8 13 12 5 4 9 14 2 6 1 7 11 14 15 5 4 16 8 7 10 9 1 13 12 2 3 6 12 3 2 6 16 4 9 10 7 8 13 1 11 15 14 5 13 15 14 16 6 5 10 9 87 12 11 1 3 2 14 11 16 87 15 5 4 13 12 2 10 916 3 15 13 5 10 9 14 16 6 11 1 3 8 7 12 4 2 16 10 8 13 12 11 15 3 14 2 6 5 4 971 8 0

Explanation / Answer

From the table we find that for all numbers from 1 to 16

we have n*1 = 1* n = n.

Hence 1 is the identity element of the group.

The answers inside the table are from 1 to 16 only. Hence the group is closed.

Finding inverse:

Inverse of a number n is m such that n*m =m*n =1

Hence we have the following table

All numbers are their own inverses except 3,9, 15, 10.

Number Inverse 1 1 2 2 3 9 4 4 5 5 6 6 7 7 8 8 9 3 10 15 11 11 12 12 13 13 14 14 15 10 16 16

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