Question: (a) Prove that a homomorphism is onto if and only if its rank equals the dimension of its codomain. (b) Conclude that a homomorphism between

(a) Prove that a homomorphism is onto if and only if its rank equals the dimension of its codomain.
(b) Conclude that a homomorphism between vector spaces with the same dimension is one-to-one if and only if it is onto.

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