I've seen a lot on this website that has helped me get started, but I have one last problem: how do I align the 0s in the first row to the matrix below them?
\documentclass{article}
\usepackage{amsmath}
\usepackage [american]{babel}
\begin{document}
\begin{equation*}
\left[
\begin{array}{cc}
\begin{matrix}
0
\end{matrix} & \begin{matrix}
0 & 0 & 0
\end{matrix} \\
\begin{matrix}
0 \\
0 \\
0 \\
\end{matrix}
& \begin{bmatrix}
n_1 & 0 & 0 \\
0 & n_2 & 0 \\
0 & 0 & n_3
\end{bmatrix}^{-1}
\end{array}\right]
\end{equation*}
\end{document}