  E. Breuillard showed that finite subsets $F$ of matrices in
$GL_d(\overline{\mathbb{Q}})$ generating non-virtually solvable groups have
normalized height $\widehat{h}(F) \ge \epsilon_d$, for some positive
$\epsilon_d >0$. The normalized height $\widehat{h}(F)$ is a measure of the
arithmetic size of $F$ and this result can be thought of as a non-abelian
analog of Lehmer's Mahler measure problem. We give a new shorter proof of this
result. Our key idea relies on the existence of particular word maps in compact
Lie groups (known as almost laws) whose image lies close to the identity
element.
