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Both of the below theorems are listed as properties 6 and 7 on the wikipedia page for the rank of a matrix.

I want to prove the following,

If A is an M by n matrix and B is a square matrix of rank n, then rank(AB) = rank(A).

Apparently this is a corollary to the theorem

If A and B are two matrices which can be multiplied, then rank(AB) <= min( rank(A), rank(B) ).

which I know how to prove. But I can't prove the first theorem. Any ideas? I would especially like to see how it is a corollary to the second theorem which the author in the book I am reading claims. Thanks for reading