Hello!
I have this to "decipher":
If 1 + ALPHA + ALPHA^2 = 0, show that ALPHA^3 = 1.
Many thanks!
I'm not sure why your topic says "matrices", but if $\displaystyle \displaystyle \alpha^3 = 1$ then
$\displaystyle \displaystyle \begin{align*} \alpha^3 - 1 &= 0 \\ \alpha^3 - 1^3 &= 0 \\ (\alpha - 1)(\alpha^2 + \alpha + 1) &= 0 \\ \alpha^2 + \alpha + 1 &= 0 \textrm{ or }\alpha - 1 &= 0 \end{align*} $