Suppose that V is a vector space and C is a scalar such that x x for every x V Prove that 1 In other words, Property O is not duplicated for any other scalar but the special scalar, 1

Question: Suppose that V is a vector space and C is a scalar such that x = x for every x V. Prove

Suppose that V is a vector space and α ∈ C is a scalar such that αx = x for every x ∈ V. Prove that α = 1. In other words, Property O is not duplicated for any other scalar but the "special" scalar, 1.

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