12. (5%) Let S be the set of all positive real numbers. Now, we want to make S as a vector space in V by asking the following definitions for vectors, vector addition, and scalar multiplication: 

ㆍ Each element of S will be considered as a "vector" in V. 

ㆍ For A, B S, a "vector sum" is defined as

 A+ B ≡ AB
where the product on the right is the usual product of two real numbers. 

ㆍFor  R (real number), and A  S, a "scalar multiplication" is defined as 

cㆍA≡ A^c, that is the real number A raised to the c power. Based on these, what is the zero vector in V?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4