Chapter 6.3, Problem 13P

Prove that the triple scalar product of $(A\times B),(B\times C),$ and $(C\times A),$ is equal to the square of the triple scalar product of $A,B,$ and $C$.

Hint: First let $(B\times C)=D,$ $(B\times C)=D,$ and evaluate $(A\times B)\times D.[\text{ See Am}\text{. J}\text{. Phys}\text{. }66,739(1998).]$