Question: Suppose that A is an m n matrix and B is an n p matrix. Prove that the column space of AB is

Suppose that A is an m × n matrix and B is an n × p matrix. Prove that the column space of AB is a subset of the column space of A, that is C(AB) ⊆ C(A). Provide an example where the opposite is false, in other words give an example where C(A) ⊈ C(AB).

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