Let \( S=\left\{\left(\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ ...
Let \( S=\left\{\left(\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right): a_{i j} \in\{-1,0,1\}\right\} \)
\( \mathrm{P} \)
W
then the number of symmetric matrices with trace equals zero, is
(1)729
(2) 189
(3) 162
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