Answer to Question #277759 in Linear Algebra for Ducky

Question

Show that a field f may be considered as a vector space over f if scalar multiplication is identified with field multiplication

Answer 1

Let V = { (a) | a in F } 

To prove; we show that vector addition is commutative.

Commutativity of addition, Here x, y are in V

(x)+(y) = (y)+(x)

(x+ y)=(y+ x): vector addition

x + (X+ y) = (X + x)+y: associative property

$\therefore$ a field f may be considered as a vector space over f