dimension and basis

["vsgdp"]

Show that all symmetric matrices from a vector space, compute its dimension, 
and show a basis in it.

I think I got the first part: I assumed the set of all square matrices 
formed a vector space, then I showed the set of symmetric matrices is a 
subspace.  However, I don't get the 2nd or 3rd.  It seems like it would have 
the same dimension as n x n matrices...I don't see where the degree of 
freedom is lost.