Let $A$ be a $2 \times 2$ matrix with all entries equal to $1.$ Define $B=\sum_{n=0}^{\infty} A^{n} / n !$. Then
- $B=e^{2} A / 2$
- $B=\left(\begin{array}{cc}1+e & e \\e & 1+e\end{array}\right)$
- $B=\dfrac{1}{2}\left(\begin{array}{ll}e^{2}+1 & e^{2}-1 \\e^{2}-1 & e^{2}+1\end{array}\right)$
- $B=\left(\begin{array}{cc}1+e^{2} & e^{2} \\e^{2} & 1+e^{2}\end{array}\right)$
- None of the above