Missing } inserted Latex - latex

Question

\begin{equation}
\tau _{2}(r_{0})=\left\{\begin{matrix}
\frac{R^{d}-r_{c}^{d}}{D_{1}}\frac{r_{0}^{-1}-a^{-1}}{-3} \\
\frac{R^{d}-r_{c}^{d}}{D_{1}}\frac{r_{c}^{-1}-a^{-1}}{-3}
\end{matrix}\right.
\end{equation}
Basically I am wrtting an equation in Latex which should be displayed in the form
But Latex reports error "Missing } inserted" on the third line. What is the problem? Thanks a lot!

Answer 1

The cases environment from the amsmath package exists for exactly this purpose:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\tau_{2}(r_{0}) =
\begin{cases}
\frac{R^{d}-r_{c}^{d}}{D_{1}}\frac{r_{0}^{-1}-a^{-1}}{-3} \\
\frac{R^{d}-r_{c}^{d}}{D_{1}}\frac{r_{c}^{-1}-a^{-1}}{-3}
\end{cases}
\end{equation}
\end{document}
This also makes it easy to add description, e.g.
\begin{equation}
\tau_{2}(r_{0}) =
\begin{cases}
\frac{R^{d}-r_{c}^{d}}{D_{1}}\frac{r_{0}^{-1}-a^{-1}}{-3} & \text{if } c = 0\\
\frac{R^{d}-r_{c}^{d}}{D_{1}}\frac{r_{c}^{-1}-a^{-1}}{-3} & \text{otherwise} \\
\end{cases}
\end{equation}

Answer 2

I made some changes to the equation and this works. Not sure if it is what you were trying to achieve
\documentclass{article}
\usepackage{graphicx}
\usepackage{amsmath}
\begin{document}
\title{Introduction to \LaTeX{}}
\author{Author's Name}
\maketitle
\[
\tau _{2}(r_{0})= \left[
\begin{array}{ccc}
\dfrac{R^{d}-r_{c}^{d}}{D_{1}} & \dfrac{r_{0}^{-1}-a^{-1}}{-3}\\
\dfrac{R^{d}-r_{c}^{d}}{D_{1}} & \dfrac{r_{c}^{-1}-a^{-1}}{-3}
\end{array}
\right]
\]
\end{document}