Solution
= Solution
A tensor is <totally antisymmetric tensor> if interchanging any two indices changes its sign. Consequently every component with repeated indices vanishes. In $\mathbb R^3$:
* for $n=2$, the general tensor is $A_{ij}=a_k\epsilon_{kij}$, with three free components;
* for $n=3$, it is $A_{ijk}=a\epsilon_{ijk}$;
* for $n>3$, every component repeats an index, so the tensor is zero.
These are all possibilities.