If the differential equation $\begin{vmatrix} f(x) & f'(x) \\ f'(x) & f''(x) \end{vmatrix} = 0$ holds for all $x$ with initial conditions $f(0) = 1$ and $f'(0) = 2$, then which of the following is true?
- A$f'(x) = -f(x)$
- B$f'(x) = f(x)$
- C$f'(x) = 2f(x)$
- D$f'(x) = 0$
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