Question: 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

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

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

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