Given a $n\times n$ matrix $B$ defined by $e^B$ by $$e^B=\sum_{j=0}^\infty \frac{B^j}{j!}$$

Let $p$ be the characteristic polynomial of $B$ Then the matrix $e^{p(B)}$ is

- $I_{n\times n}$
- $e \times I_{n\times n}$
- $e \times I_{n\times n}$
- $0_{n\times n}$
- $\pi \times I_{n\times n}$

Choose the correct option from above.