Suppose that $V$ is a vector space and $\alpha\in\complexes$ is a scalar such that $\alpha\vect{x}=\vect{x}$ for every $\vect{x}\in V$. Prove that $\alpha = 1$. In other words, Property O is not duplicated for any other scalar but the “special” scalar, 1. (This question was suggested by James Gallagher.)