The problem statement is as below.

Represent the following formulas with the elements which are of the linear representations of $GF(2^2)$ where the root $\alpha$ satisfies $x^2+x+1=0$ .

$(1)$ $\alpha^4$

$(2)$ $\alpha^2-(\alpha-1)$

$(3)$ $\frac{\alpha}{\alpha^4}$

I have the following formula but I don't know how should I use it.

$GF(2^2)=\{0,1,\alpha,\alpha+1\}$ $,(\alpha^2+\alpha+1)$

Can someone let me know the solutions or some website that explain about the solutions?