) Let V be a vector space over a field F. Suppose that T₁: V → V and T₂: V → V are linear maps so that for every v EV there is some a EF with T₂(T₁(v)) = av. i. Show that there is a single a € F, such that for every v V, T₂(T₁(v)) = av. ii. Assuming that this a is not 0, show that both T₁ and T₂ must be isomorphisms.

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