Each group will be assigned one of the following matrices.
\[
A_1\doteq
\begin{pmatrix}
0&-1\\
1&0\\
\end{pmatrix}
\hspace{2em}
A_2\doteq \begin{pmatrix}
0&1\\
1&0\\ \end{pmatrix}
\hspace{2em}
A_3\doteq \begin{pmatrix}
-1&0\\
0&-1\\ \end{pmatrix}
\]
\[
A_4\doteq \begin{pmatrix}
a&0\\
0&d\\ \end{pmatrix}
\hspace{2em}
A_5\doteq \begin{pmatrix}
3&-i\\
i&3\\ \end{pmatrix}
\hspace{2em}
A_6\doteq \begin{pmatrix}
0&0\\
0&1\\ \end{pmatrix}
\hspace{2em}
A_7\doteq \begin{pmatrix}
1&2\\
1&2\\ \end{pmatrix}
\]
\[
A_8\doteq \begin{pmatrix}
-1&0&0\\
0&-1&0\\
0&0&-1\\ \end{pmatrix}
\hspace{2em}
A_9\doteq \begin{pmatrix}
-1&0&0\\
0&-1&0\\
0&0&1\\ \end{pmatrix}
\]
\[
S_x\doteq \frac{\hbar}{2}\begin{pmatrix}
0&1\\
1&0\\ \end{pmatrix}
\hspace{2em}
S_y\doteq \frac{\hbar}{2}\begin{pmatrix}
0&-i\\
i&0\\ \end{pmatrix}
\hspace{2em}
S_z\doteq \frac{\hbar}{2}\begin{pmatrix}
1&0\\
0&-1\\ \end{pmatrix}
\]
For your matrix:
If you finish early, try another matrix with a different structure, i.e. real vs. complex entries, diagonal vs. non-diagonal, \(2\times 2\) vs. \(3\times 3\), with vs. without explicit dimensions.