JAMB 1994 · UME · Q23

The table shows multiplication modulo 10 on the set $S = \{2, 4, 6, 8\}$ . Find the inverse of 2.

$\otimes$	2	4	6	8
2	4	8	2	6
4	8	6	4	2
6	2	4	6	8
8	6	2	8	4

Worked solution (try it first)

Find the identity first: the row for 6 reads 2, 4, 6, 8, the same as the heading, so 6 is the identity.
The inverse of 2 is the element that combines with 2 to give the identity 6.
In the row for 2, the 6 is under the column 8: $2 \otimes 8 = 16$ , which is 6 modulo 10.
So the inverse of 2 is 8, option D.