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 ?

If $A^4=-A$, then $$A^{482}=A^2A^{480}=A^2(A^4)^{120}=A^2(-A)^{120}=A^2(A^4)^{30}=A^2(-A)^{30}=A^{32}=(A^4)^8=(-A)^8=(A^4)^2=(-A)^2=A^2$$
