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 is an M by n matrix and is a square matrix of rank n, then = .
Apparently this is a corollary to the theorem
If and are two matrices which can be multiplied, then .
which I know how to prove. But I can't prove the first theorem. Any ideas?