Question: I am using the `amsmath` package.
My code is

```
\begin{center}

   \left $\begin{bmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bmatrix}$

\end{center}
\begin{center}
\right $\begin{bmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bmatrix}$
    \end{center}

```

Thanks for any help!

Answer: 
* Please, always provide complete small document called MWE (Minimal Working Example) which reproduce your problem.
* your question is not entirely clear, so I guess, that you after the following:

[![enter image description here](https://i.stack.imgur.com/V6mKz.png)](https://i.stack.imgur.com/V6mKz.png)

MWE:

```
\documentclass{article}
\usepackage{amsmath}

\begin{document}
\[
    \begin{bmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bmatrix}%
    \begin{bmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bmatrix}
\]
\end{document}

```

Comparison of above code with your code fragment shows, that it contain a lot of clutter: `\left`, `right`, `\begin{center} ... \end{center}`. In above MWE used symbols `\[` and `\]` switch from "text mode" to "math mode". They are equivalent to `\begin{equation*}` and `\end{equation*}` respectively.
I have created a minimal working example (with a comma between the two matrices) to have **the matrices on the same line in LaTeX.** However I would to use a small matrix when you use `$...$`.

```
\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\begin{document}
Some $\begin{bmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bmatrix}, \begin{bmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bmatrix}$ test after two matrices.
\[\begin{bmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bmatrix}, \quad \begin{bmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bmatrix}\]
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/61zAU.png)](https://i.stack.imgur.com/61zAU.png)

Using `bsmallmatrix` enviroment with `mathtools` package.

```
\documentclass[a4paper,12pt]{article}
\usepackage{mathtools}% for "bsmallmatrix" environment
\usepackage{amssymb}
\begin{document}
Some $\begin{bsmallmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bsmallmatrix},\begin{bsmallmatrix}
    u_1 & u_2\\ u_3 & u_4
    \end{bsmallmatrix}$ test after two matrices.
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/yZj6y.png)](https://i.stack.imgur.com/yZj6y.png)