Past exam of the mathematics course of the University of Cambridge / 2010 / ii / Paper 4 / 39A / c / Solution

An A-stable method must satisfy $|P_s(z)|\le 1$ for every $z$ with nonpositive real part. A consistent explicit Runge-Kutta method has $P_s^{\prime }(0)=1$, so its stability polynomial is nonconstant. Along the negative real axis the leading term of any nonconstant polynomial has magnitude tending to infinity. HenceThe positive order assumption in the question supplies the required consistency.