Let A be an n × n matrix. Define the determinantal rank detrankA to be the greatest value of r such that there is an r × r submatrix B of A (that is, a matrix B obtained by deleting n − r rows and n − r columns from A) such that detB 0. Show that detrankA = rankA.
Genuinally have no idea where to start, I can't even see that this is true so haven't got any ideas. Help appreciated!