The first IE of Be is greater than that of B because Be has stable complete electronic configuration $\left(1 s^2 2 s^2\right)$, which require more energy to remove the first electron from its valence shell, whereas, B has electronic configuration $1 s^2 2 s^2 3 s^1$ which require lesser energy than that of Be. In atoms with more than one electron, $2 s$-orbital is lower in energy than $2 p$-orbital.
So, $\mathrm{A}$ is true, but $\mathrm{R}$ is false.