Semidirect product of cyclic Lie ring of prime-square order and cyclic Lie ring of prime order

Definition
Let $$p$$ be a prime number]. The nontrivial semidirect product of cyclic Lie ring of prime-square order and cyclic Lie ring of prime order is a [[Lie ring of order $$p^3$$ given by the following presentation:

$$\langle a,b \mid p^2a = pb = 0, [a,b] = pa \rangle$$