Number of solutions of Determinant

Algebra Level pending

\[\left| \begin{matrix} \arcsin { x } & \arcsin { 2x } & \arcsin { 3x } \\ \arcsin { 3x } & \arcsin { x } & \arcsin { 2x } \\ \arcsin { 2x } & \arcsin { 3x } & \arcsin { x } \end{matrix} \right| =0 \] If the number of solutions of the above determinant is \(A\), find \(\dfrac{2016}A \).

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