Two binary operations $\oplus$ and $^\ast$ are defined over the set $\{a, e, f, g, h\}$ as per the following tables
$\oplus$ |
a |
e |
f |
g |
h |
a |
a |
e |
f |
g |
h |
e |
e |
f |
g |
h |
a |
f |
f |
g |
h |
a |
e |
g |
g |
h |
a |
e |
f |
h |
h |
a |
e |
f |
g |
$^\ast$ |
a |
e |
f |
g |
h |
a |
a |
a |
a |
a |
a |
e |
a |
e |
f |
g |
h |
f |
a |
f |
h |
e |
g |
g |
a |
g |
e |
h |
f |
h |
a |
h |
g |
f |
e |
Thus, according to the first table $f \oplus g = a$, while according to the second table $g \ast h = f$, and so on. Also, let $f^2 = f\ast f, \: g^3 = g \ast g \ast g$, and so on.
What is the smallest positive integer n such that $g^n = e?$
- $4$
- $5$
- $2$
- $3$