This question Im really lost on, a bit of guidance would be great!

Let $\displaystyle J_n$ be the $\displaystyle R$-vector space with basis $\displaystyle B = \{1,cos(x),sin(x),...,cos(nx),sin(nx)\}$. For a fixed positive real number $\displaystyle a$, define $\displaystyle D \in Hom(J_n,J_n)$ by $\displaystyle D(f) = f'' + a^2f$. For which $\displaystyle a$ is $\displaystyle D$ invertible?