= Solution
The <stability function> of a <Runge-Kutta method> is $R(z)=1+zb^T(I-zA)^{-1}\mathbf1$. Substitution gives
$$
\boxed{R(z)=\frac{1+z/2+z^2/12}{1-z/2+z^2/12}.}
$$
Writing the numerator and denominator as $N(z)$ and $D(z)$,
$$
|D(z)|^2-|N(z)|^2=-2\operatorname{Re}z\left(1+\frac{|z|^2}{12}\right).
$$
The denominator has zeros $3\pm i\sqrt3$, both in the right half-plane. Therefore $|R(z)|\leq1$ throughout the closed left half-plane, with strict inequality in its interior. The method is \b[<A-stable>]. Since $R(z)\to1$ at infinity, it is not <L-stable>.
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