Questions on column spaces

Question

The following are some true false questions that are homework problems. I have stated both the answer and the reason.
1. If the columns of a matrix are dependent, so are the rows. (True as row rank=column rank).
2. The column space of a $2*2$ matrix is same as its row space. (True as they are square).
3. The column space of a $2*2$ matrix has the same dimension as its row space. (True. r=m=n, the number of pivots is same in both cases).
4. The columns of a matrix are a basis for the column space. (False. Not always. Only linearly independent columns that span the column space forms a basis).