Let $V$ be the vector space of all real polynomials of degree $\leq 10$. Let $Tp(x)=p'(x)$ for $p\in V$ be a linear transformation from $V$ to $V$. Consider the basis $\{1,x,x^2,\cdots x^{10}\}$ of $V$. Let $A$ be the matrix of $T$ with respect to this basis. Then which of the following is correct?

- Trace $A=1$
- There is no $m\in \mathbb{N}$ Such that $A^m=0$.
- $\det{A}=0$.
- $A$ has a nonzero eigenvalue.