Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 3 / 12A / c / Solution

Isotropic means invariant under every proper rotation. The general ranks $0,1,2,3$ are respectively a scalar $a$, zero, $b{\delta }_{ij}$, and $c{\epsilon }_{ijk}$ (for full orthogonal invariance the last must also vanish).

Solved by gpt-5.6-sol high.