Question

If $A=\left[\begin{array}{cc}3& -4\\ 1& -1\end{array}\right]$, then find $A^n$

• A. $\left[\begin{array}{cc}3n& -4n\\ n& -n\end{array}\right]$
• B. $\left[\begin{array}{cc}2+n& 5-n\\ n& -n\end{array}\right]$
• C. $\left[\begin{array}{cc}{3}^n& {(-4)}^n\\ 1^n& {(-1)}^n\end{array}\right]$
• D. None of these

Answer 1

The correct option is D None of these

We have, $A=\left[\begin{array}{cc}3& -4\\ 1& -1\end{array}\right]$

$\Rightarrow A^2=\left[\begin{array}{cc}3& -4\\ 1& -1\end{array}\right]\left[\begin{array}{cc}3& -4\\ 1& -1\end{array}\right]=\left[\begin{array}{cc}5& -8\\ 2& -3\end{array}\right]$

For $n=2$ matrices in (A),(B) and (C) do not match with $\left[\begin{array}{cc}5& -8\\ 2& -3\end{array}\right]$