I'm a bit confused about an exercise I read. Namely, T. Y. Lam's A First Course in Noncommutative Rings has the following on page $23$ Ex. $1.10$.
Let $p$ be a fixed prime. Show that there exists a noncommutative ring (with identity) of order $p^3$.
Well, this implies that there is a noncommutative ring with identity of order $8<16$, which contradicts with benh's answer given in smallest non commutative ring with unity . So have I understood correctly that there is a mistake in Lam's exercise?