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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