The n by n matrix often called J_n, all of whose entries are 1, has all rows equal.
Row reduction stops after one step: subtracting the first row from the rest leaves n -1 0 rows.
Its rank is one and its nullity n -1.
Its range is is one dimensional consisting of all multiples of the vector all of whose components are 1.
Its null space consists of all vectors whose components sum to zero, which is also its kernel.