Q: The ring {0, 2, 4 , 6, 8] under addition and multiplication modulo 10 has a unity. Find it.
A: By definition we know that the unity of a ring is a nonzero element that is an identity under multiplication (of the ring).
So we can test each element of the ring {0, 2, 4 , 6, 8] to see which element satisfies these conditions.
2*2 = 4 4 modulo 10 = 4 \neq 2
