Apparently text is resized in one way and math in other way. However, the commands to resize math do not work well on a matrix; it appears barely smaller and unexpectedly shifted down. The commands to resize text also "work well" to resize a matrix except that it give a warning that you are doing it wrong.
LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 16.
So, what is a proper way to resize a matrix that actually works?
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\begin{document}
Properly resize variable: $x$ $\scriptscriptstyle{x}$
Properly resize matrix: $\begin{bmatrix}a & b\\ c & d\end{bmatrix}$ $\scriptscriptstyle{\begin{bmatrix}a & b\\ c & d\end{bmatrix}}$
Improperly resize matrix: $\begin{bmatrix}a & b\\ c & d\end{bmatrix}$ $\scriptsize{\begin{bmatrix}a & b\\ c & d\end{bmatrix}}$
\end{document}
