Question

If $A =\begin{pmatrix} a & 1 \\ 0 & a \end{pmatrix}$, then for any $n \in N , A ^{ n }$ equals-

• A. $\begin{pmatrix} na & n \\ 0 & na \end{pmatrix}$
• B. $\begin{pmatrix}a^n & n a^{n-1} \\ 0 & a^n\end{pmatrix}$
• C. $\begin{pmatrix}\text { na } & 1 \\ 0 & \text { na }\end{pmatrix}$
• D. $\begin{pmatrix}a^n & n \\ 0 & a^n\end{pmatrix}$

Answer 1

Answer: (B)

Correct answer is (b) $\begin{pmatrix}a^n & n a^{n-1} \\ 0 & a^n\end{pmatrix}$