System of differential equations of second order $X''(t) = -(A^2)X(t)$

Question

How do I solve problems of the form $$X''(t) = -(A^2)X(t),$$ where $X$ is a $2 \times 1$ matrix and $A$ is a $2 \times 2$ matrix? We're given $X(0)$ and $X'(0)$.