Reflection Rule for Gaussian Binomial Coefficients

Theorem
Let $q \in \R_{\ne 1}, n \in \Z_{>0}, k \in \Z$.

Then:
 * $\dbinom n k_q = q^{k \paren {n - k} } \dbinom n k_{q^{-1} }$

where $\dbinom n k_q$ is a Gaussian binomial coefficient.