Float matrix left among other matrices

Question

I'd like to float one matrix left among the others, and make the text grey. Currently, I can only simulate this by adding the correct \hspace*{} after my first matrix that I would like to align left.
My current code looks like such,

 \documentclass{article}
 \usepackage[utf8]{inputenc}
 \usepackage{mathtools}
 \usepackage{amsmath}
 \usepackage{amssymb}
 \DeclarePairedDelimiter\ket{\lvert}{\rangle}
 \begin{document}    
 \begin{equation}
 \begin{matrix}
  \ket{11}\\
  \ket{01}\\
  \ket{10}\\
  \ket{00}
\end{matrix} \hspace*{50pt}
 \begin{pmatrix}
  0\\
  0\\
  1\\
  0
\end{pmatrix} 
 \begin{pmatrix}
  0 & 0 & 1 & 0\\
  0 & 1 & 0 & 0\\
  1 & 0 & 0 & 0\\
  0 & 0 & 0 & 1
 \end{pmatrix}
 =
  \begin{pmatrix}
  1\\
  0\\
  0\\
  0
\end{pmatrix} 
\end{equation}
\end{document} 

and yields the following

Concluding; how do I left align/float the first matrix and make the text grey?

Answer 1

Use the flalign environment and {\color{gray} ket matrix } (requires color or xcolor. Note you don't have to load amsmath since mathtools does it:

 \documentclass{article}
 \usepackage[utf8]{inputenc}
 \usepackage{xcolor} %
 \usepackage{mathtools}%
 \usepackage{amssymb}
 \DeclarePairedDelimiter\ket{\lvert}{\rangle}
 \begin{document}

 \begin{flalign}
  &{\color{gray} \begin{matrix}
  \ket{11}\\
  \ket{01}\\
  \ket{10}\\
  \ket{00}
\end{matrix}} %
& \begin{pmatrix}
  0\\
  0\\
  1\\
  0
\end{pmatrix}
 \begin{pmatrix}
  0 & 0 & 1 & 0\\
  0 & 1 & 0 & 0\\
  1 & 0 & 0 & 0\\
  0 & 0 & 0 & 1
 \end{pmatrix}
  & =
  \begin{pmatrix}
  1\\
  0\\
  0\\
  0
\end{pmatrix}
 & & %
 \end{flalign}

\end{document} 

Answer 2

The xcolor package's \textcolor{<color>}{<text>} command could simply help you with the color. The {\color{<color>} text}, is another option, but I like the former more.