  Let $M_q(n)$ be the standard quantized matrix algebra, introduced by Faddeev,
Reshetikhin, and Takhtajan. It is shown, by constructing an appropriate
monomial ordering $\prec$ on its PBW $K$-basis ${\cal B}$ , that $M_q(n)$ is a
solvable polynomial algebra. Consequently, further structural properties of
$M_q(n)$ and their modules may be established and realized in a
constructive-computational way.
