Solution
= Solution
\b[Yes.] If $g$ generates the <cyclic group> $C_n$, define the one-dimensional <complex representation>
$$
\rho(g)=e^{2\pi i/n}.
$$
It is irreducible because it is one-dimensional, and it is faithful because the displayed scalar has multiplicative order $n$. Thus every $C_n$, including the trivial case $n=1$, has a faithful irreducible representation.