Let V, W be finite-dimensional vector spaces.(a) Suppose that there exist an injective g ∈ L (V, W) and an injective g` ∈ L (W, V ). Prove that V ∼= W.(b) Can it happen that there exist a surjective h ∈ L (V, W) and an injective h`∈ L (W, V ) but V and W are not isomorphic? Prove or provide a counterexample.

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