When we say that the identity and inverse element in a vector space is unique, does it mean that those elements are the same for all x in V? or does it mean that each x has its own unique identity or inverse element? moreover, is there a geometric way of explaning what a field is? because I got confused about the scalar multiplication of a vector space that b in F and c in V which give bc in V.. and also, did anyone used Linear Algebra by Friedberg, Insel and Spense before? What do you think about the book?