If the columns of A span Rn, then the columns of A form a basis of Rn.

Also, I need to go the other way as well to make sure it is logically equivalent....I also need to show:

If the columns of A form a basis of Rn, then the columns of A span Rn.

I want to do a proof by contradiction...but not sure how.....This is sooooo confusing...thanks in advance