$$ A = \begin{pmatrix}B&C\\D&E\end{pmatrix} $$ where B is a $m \times n$ , C is a $ m \times k$ , D is a $ k \times n$ and E is a $ k \times k$ matrix. If E is an invertible matrix, what can we say about rank(A)?
I just know that the rank of a matrix is equal to the maximum number of linearly independent rows (or columns). I have no idea what to do!
Hint: There are at least as many independent rows for $A$ as in $E$.