$\displaystyle A = \left( {\begin{array}{rr}

{-10} & {-18} \\

9 & 17 \\

\end{array} } \right)$

a) Find Y such that $\displaystyle Y^{-1}AY$ is diagonal.

b) Find C such that $\displaystyle C^3 = A$

For a I get $\displaystyle Y = \left( {\begin{array}{rr}

2 & 1 \\

-1 & -1 \\

\end{array} } \right)$

I can't figure out b. Does it involve the Cayley-Hamilton theorem at all? I've only used that for solving $\displaystyle C=A^3$ not this way round. Thanks!