Let V and W be finite-dimensional vector spaces over the field F such that dim V = dim W. If T is a linear transformation from V into W (i) T is invertible. (ii) T is non-singular. (iii) T is onto,

,now prove that (A) (i) is true Iff (ii) is true

(B) (ii) is true Iff (iii) is true

(C) (iii) is true Iff (i) is true

Prove all the above 3 parts (A,B.C).