Solution
= Solution
In components the <scalar triple product> is $A_i\epsilon_{ijk}B_jC_k$. A cyclic <permutation> has positive <sign of a permutation>, so $\epsilon_{ijk}=\epsilon_{kij}$. Relabelling the summed indices therefore gives
$$
A_i\epsilon_{ijk}B_jC_k=\epsilon_{kij}A_iB_jC_k=(A\times B)_kC_k,
$$
which proves $A\cdot(B\times C)=(A\times B)\cdot C$. Equivalently both expressions are the same three-column <determinant>.