If $$ A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right] $$, then $$ A^n $$ for any natural number is
\(A^2 = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}\) and \(A^3 = \begin{pmatrix} 1 & 3 \\ 0 & 1 \end{pmatrix}\).
By induction, \(A^n = \begin{pmatrix} 1 & n \\ 0 & 1 \end{pmatrix}\).
Answer: (B)
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