$\left\{ \begin{align}  & \left| \left| B \right|A \right|={{\left| B \right|}^{3}}\left| A \right| \\  & \left| \left| A \right|B \right|={{\left| A \right|}^{3}}\left| B \right| \\ \end{align} \right.\Rightarrow \left| \left| B \right|A \right|+\left| \left| A \right|B \right|={{\left| B \right|}^{3}}\left| A \right|+{{\left| A \right|}^{3}}\left| B \right|$ $=\left| {{B}^{3}}A \right|+\left| {{A}^{3}}B \right|$