Introduction : Here we shall explain How to find matrix power through an example. Question : If \[A=\left(\begin{matrix}3&-4\\1&-1\end{matrix}\right)\] then find \(A^n\) Solution : Given matrix \[A=\left(\begin{matrix}3&-4\\1&-1\end{matrix}\right)\] second power of A \[A^2=\left(\begin{matrix}3&-4\\1&-1\end{matrix}\right)\left(\begin{matrix}3&-4\\1&-1\end{matrix}\right)=\left(\begin{matrix}5&-8\\2&-3\end{matrix}\right)\] Third power of A \[A^3=A^2A=\left(\begin{matrix}5&-8\\2&-3\end{matrix}\right)\left(\begin{matrix}3&-4\\1&-1\end{matrix}\right)=\left(\begin{matrix}7&-12\\3&-5\end{matrix}\right)\] Fourth power of A…
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