Past exam of the mathematical methods I course of the University of Oxford / 2014 resit / 12 / iv / Solution

If two indices of the n-dimensional Levi-Civita symbol are equal, exchanging them leaves the component unchanged. Antisymmetry of a multilinear map simultaneously negates it, so $ϵ=-ϵ$. Over the real numbers this implies $\boxed{ϵ=0}$.