Given a 2n x 2n matrix M which can be decomposed into to matrices M = [A B] where A and B are 2n x n matrices. Rank(A) = n, Rank(B) = n and also ANY n rows of A are linearly independent and also any n rows of B. Also, any n rows of the 4n x n matrix

[A]

B]

are linearly independent.

Is it true that Rank(M) = 2n and how can it be shown?