literally have no clue on how to do this one... :'(

Prove that if A and B are n x n matrices and if rank(A) = n and rank(B) = n then rank(AB) = n.

any help would be much appreciated here as i have a test tomorrow!

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- March 6th 2011, 12:22 PMsituationrank theory
literally have no clue on how to do this one... :'(

Prove that if A and B are n x n matrices and if rank(A) = n and rank(B) = n then rank(AB) = n.

any help would be much appreciated here as i have a test tomorrow! - March 6th 2011, 12:57 PMTheEmptySet
- March 6th 2011, 01:24 PMHallsofIvy
Another way- the "rank" of a linear transformation, A, from vector space V to itself is the dimension of A(V). Here, A is given by an n by n matrix so it is from to . Since the rank of A is n, . Similarly, the rank of B is n so that . Putting those together, AB maps into all of : and so AB has rank n.

- March 6th 2011, 02:31 PMsituation