Let $\mathrm{V}$ and $\mathrm{W}$ be finite dimensional vector spaces over $\mathrm{F}$, and $\mathrm{T}$ is a function from $\mathrm{V}$ to $\mathrm{W}$. In this regard, some of the following statements are correct.
- If $\mathrm{T}$ is linear, then $\mathrm{T}$ preserves sums and scaler products.
- $T$ is one-to-one, if and only if, there is a vector $x$ such that $T(x)=0$ when $x=0$
- If $T(x+y)=T(x)+T(y)$, then $T$ is linear.
- If $T$ is linear, then $T\left(\mathbf{0}_{V}\right)=\mathbf{0}_{W}$
Choose the most appropriate answer from the options given below:
- A and D only
- A and B only
- B and D only
- C and D only
