Getting error says "missing $ inserted" in latex - latex

Question

Getting error message that there is a missing $ inserted
I've tried adding in front of n and the other one in front of \end{pmatrix} but it doesn't work.
\begin{equation} n_1=\begin{pmatrix}2\\1\\-1\end{pmatrix}\times \begin{pmatrix}3\\-1\\0\end{pmatrix} = \begin{vmatrix}$e_1&e_2&e_3$\\2&1&-1\\3&-1&0\end{vmatrix}=\begin{pmatrix}-1\\-3\\-5\end{pmatrix} \end{equation}
\begin{equation}n_2=\begin{pmatrix}1\\1\\-1\end{pmatrix}\times \begin{pmatrix}2\\-1\\0\end{pmatrix} = \begin{vmatrix}$e_1&e_2&e_3$\\1&1&-1\\2&-1&0\end{vmatrix}=\begin{pmatrix}-1\\-2\\-3\end{pmatrix}\end{equation}

Answer 1

The following code segment
\documentclass[a4papaer, 11pt]{article}
\usepackage[top=3.5cm, bottom=3.5cm, left=3.0cm, right=3.0cm]{geometry}
\usepackage{amsmath}
\begin{document}
\begin{equation} n_1=
\begin{pmatrix}
2\\1\\-1
\end{pmatrix}\times
\begin{pmatrix}
3\\-1\\0
\end{pmatrix} =
\begin{vmatrix}
e_1&e_2&e_3 \\
2&1&-1\\
3&-1&0
\end{vmatrix} =
\begin{pmatrix}
-1\\-3\\-5
\end{pmatrix}
\end{equation}
\begin{equation}
n_2=
\begin{pmatrix}
1\\1\\-1
\end{pmatrix}\times
\begin{pmatrix}
2\\-1\\0
\end{pmatrix} =
\begin{vmatrix}
e_1&e_2&e_3\\
1&1&-1\\
2&-1&0
\end{vmatrix}=
\begin{pmatrix}
-1\\-2\\-3
\end{pmatrix}
\end{equation}
\end{document}
results in the matrices from this image. Was that the result you were hoping for?