Find the Matrix $A^{482}$ in terms of $A$ Given $$A=\begin{bmatrix}
-4 & 3\\ 
-7 & 5
\end{bmatrix}$$ Find $A^{482}$ in terms of $A$
I tried using Characteristic equation of $A$ which is $$|\lambda I-A|=0$$ which gives
$$A^2=A-I$$ so $$A^4=A^2A^2=(A-I)^2=A^2-2A+I=-A$$ so
$$A^4=-A$$ but $482$ is neither multiple of $4$ nor Power of $2$, How can I proceed ?

See if you calculate $A^3$ you get $A^3=-I$ thus now raising both sudes to $160$ we get $A^{480}=I$ so $A^{482}=A^2$ thus $A^2=A-I$
