9. let u and v be vector spaces.over the field p, f from u into v, there is a unique lincar transformation t(8)jku)-s[t(")]¥g e v and u e u, whiere u and v are

9. Let U and V be vector spaces.over the field P, F from U into V, there is a unique lincar transformation T(8)Jku)-s[T(")]¥g e V and u e U, whiere U and V are dual of U and V respectively. Then T is called : (A) transpose of T (8) dunl of ()complement of Tr (D) inverse of T 80. Let G be a group and d eG. Then normalizer of a is given by A)xeG: = xa) (8) xeG: x = e (C) xe G:xa= e (D) None of these 81. The set of Gaussian integers J[= {a + ib: a, be Z} with ordinary adition multiplication of complex numbers is: (A) a field B) an integral domain (C)Both (A) and (B) (D) None of these 82. A linear transformation T: 0Vis one-to-one if and only if kernel of T is et to (A) U (B) V )0 (D) None of these