Well, I figured it out if anyone is interested.
Using the argument here (http://en.wikipedia.org/wiki/Rank_%28linear_algebra%29) under rank of a "Gram matrix" with real entries and the rank + nullity equals number of columns theorem you can show the rank of A equals the rank of A'*A.
Thus, the...
Let A be an n x p matrix with real entries and A' be its transpose. Is the column space of A'*A the same as the column space of A'. Obviously, the column space of A'*A is a subset of the column space of A' but can I show the other way? Thanks!