If the matrix \(\mathrm{A}=\left(\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 2 & 0 & 2\end{array}\right)\), then \(\mathrm{A}^{\mathrm{n}}=\left(\begin{array}{lll}\mathrm{a} & 0 & 0 \\ 0 & \mathrm{a} & 0 \\ \mathrm{~b} & 0 & \mathrm{a}\end{array}\right), \mathrm{n} \in \mathrm{N}\) where
(A) \(a=2 n, b=2^{n}\)
(B) \(a=2^{n}, b=2 n\)
(C) \(\mathrm{a}=2^{\mathrm{n}}, \mathrm{b}=\mathrm{n} 2^{\mathrm{n}-1}\)
(D) \(a=2^{n}, b=n 2^{n}\)
