Composition of linear maps I have question as follows:
Let $V$  be a vector space of dimension  3 over $\Bbb R $  and let t $\in$ $\mathcal L (V,V)$ have eigenvalue $-2,1,2$ . Use the Calyey-Hamilton theorem to find $t^4$ 
I know that $(t-2)(t-1)(t+2) =0$ so
$t^3 = t^2 +4t -4id$
I am unsure how to proceed 

Hint
Write the long division of $x^4$ by the characteristic polynomial.
Details
We find
$$x^4=(x+1)\chi_t(x)+5x^2-4$$
so by the Cayely-Hamilton theorem we have
$$t^4=5t^2-4\operatorname{Id}$$
