How to find matrix power

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 \[A^4=A^3A=\left(\begin{matrix}7&-12\\3&-5\end{matrix}\right)\left(\begin{matrix}3&-4\\1&-1\end{matrix}\right)=\left(\begin{matrix}9&-16\\4&-7\end{matrix}\right)\] . . . Now to…

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