| (A) | 32 | (B) | 8 | (C) | 16 | (D) | 24 |
Consider the matrix
$$P = \left( \begin{array} { l l l }
2 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 3
\end{array} \right)$$
Let the transpose of a matrix $X$ be denoted by $X ^ { T }$. Then the number of $3 \times 3$ invertible matrices $Q$ with integer entries, such that
$$Q ^ { - 1 } = Q ^ { T } \text { and } P Q = Q P$$
is
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | }
\hline
(A) & 32 & (B) & 8 & (C) & 16 & (D) & 24 \\
\hline
\end{tabular}
\end{center}