It is given that rank of A is r. Then A has rr independent columns. Let B be the submatrix formed by those rr columns of A. Clearly the rank of B is r. We know that rank of a matrix is equal to dimension of the row space of that matrix. Therefore dimension of the row space of B also r. Therese rr rows are linearly independemmt. Form the submatrix B if we choose particularly those r rows, then is an r×r submatrix which is invertible.