problem in alignment of arrays [duplicate]

Question

\documentclass[12pt]{report}
\usepackage{amsfonts,amsmath,mathtools}
\begin{document}
\begin{align*}
0\longrightarrow S
\xrightarrow{
\begin{array}{c}
xyz\\
\end{array}
\left[\begin{array}{rrr}
1 \\-1 \\1 \\
\end{array}
 \right]
 \begin{matrix}
\\yz\\xz\\xy
 \end{matrix}
}S^3
\xrightarrow{
\begin{array}{rrr}
yz&xz&xy\\
\left[\begin{array}{rrr}
0&1&1\\
1&0&-1\\
-1&-1&0\\
\end{array}
\right]
\end{array}
}S^3
\end{align*}
\end{document}

I want to align the row yz xz xy with the top row of the 3 by 3 matrix given in the code

Answer 1

Maybe you want something like this?

\documentclass[12pt]{report}
\usepackage{amsfonts, mathtools}

\begin{document}

\begin{align*}
  0 ―――→ S
  \xrightarrow{
  xyz
  \begin{bsmallmatrix*}[r]
  1 \\-1 \\1
  \end{bsmallmatrix*}
  \begin{smallmatrix}
  yz\\xz\\xy
  \end{smallmatrix}%
  }S³
  \xrightarrow{
  \begin{matrix}
  \begin{smallmatrix*}
    & yz & & zx & & xy \end{smallmatrix*} \\
  \begin{bsmallmatrix*}[r]
  0&1&1\\
  1&0&-1\\
  -1&-1&0\\
  \end{bsmallmatrix*}
  \end{matrix}
  }S³
\end{align*}

\end{document}