This is a pattern even school kids could discover (when gently pointed to). I never did conciously, and cannot remember to have been pointed to explicitly, neither at school nor later:
$$\color{red}{\mathbf{2}}\cdot 9 = 1\color{red}{\mathbf{8}}$$ $$\color{red}{\mathbf{8}}\cdot 9 = 7\color{red}{\mathbf{2}}$$
$$\color{blue}{\mathbf{3}}\cdot 9 = 2\color{blue}{\mathbf{7}}$$ $$\color{blue}{\mathbf{7}}\cdot 9 = 6\color{blue}{\mathbf{3}}$$
$$\color{green}{\mathbf{4}}\cdot 9 = 3\color{green}{\mathbf{6}}$$ $$\color{green}{\mathbf{6}}\cdot 9 = 5\color{green}{\mathbf{4}}$$
which may come as kind of a miracle when first discovering it.
In mathematical terms
$$\boxed{a\cdot (10-1) \equiv b \mod 10\ \ \ \ \Leftrightarrow\ \ \ \ \ b\cdot (10-1) \equiv a \mod 10 \\ a\cdot (10-1) \equiv b \mod 10\ \ \ \ \Leftrightarrow\ \ \ \ \ a + b = 10 \equiv 0 \mod 10}$$
This holds not only for $10$ but for every $p \in \mathbb{N}$, i.e. in every "number system":
$$\boxed{a\cdot (p-1) \equiv b \mod p\ \ \ \ \Leftrightarrow\ \ \ \ \ b\cdot (p-1) \equiv a \mod p \\ a\cdot (p-1) \equiv b \mod p\ \ \ \ \Leftrightarrow\ \ \ \ \ a + b = p \equiv 0 \mod p}$$
and is responsible for the fact that the graphical multiplication tables of $\mathbb{Z}/p\mathbb{Z}$ always looks the same for $p-1$:
I wonder if there are attempts (in educational research and literature) to make use of the simple observability of the pattern above to explain to (clever) school kids that the observed regularity is not by pure coincidence, why it is so, and what it does "mean".