Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / 49 / b / i / Solution

For representation spaces $V,W$, the tensor product of group representations acts on product basis vectors throughIts character is the trace. Summing diagonal elements explicitly,No step assumes one-dimensional matrices, so the result applies to both degenerate and nondegenerate representations.