Denote by $R$ the set of all functions from the set $\lbrace -10, -6, -5, 3 \rbrace$ to the ring $\mathbb{Z}_{18}$. FACT: $R$ becomes a ring under the following operations:

$$f + g: a \mapsto f(a) + g(a)$$
$$f * g: a \mapsto f(a)g(a)$$
(a) Is $R$ a commutative ring?   ? Yes No

(b) How many units are there in $R$?

(c) Give an example of a non-zero $f \in R$ that is a zero-divisor by filling in the following table:

$x$	$f(x)$
$-10$
$-6$
$-5$
$3$