Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 343 / 3 / a / Solution

There are only two one-site matrices, so they cannot span the four-dimensional virtual matrix algebra. For two sites,Every overlap $⟨s_i|j⟩$ is nonzero, and the four outer products $|i⟩⟨s_j|$ are linearly independent. Hence