Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 15E / b / Solution

Conjugating a reflection by a unitary reflects in the transported vector. Since $A|0^n⟩=|\Omega ⟩$,and every vector orthogonal to $|\Omega ⟩$ is fixed. Hencein particular both sides act identically on $|\Omega ⟩$.