Let G be the profinite free group on 2 generators, $A=G/[G,[G,G]],B=G/[[G,G],[G,G]]$, then what is the struct of the groups $A$ and $B$?

I was heard about that $A$ is isomorphic to the group of such (3*3 below) matrices with coefficients in $\hat{\mathbb{Z}}$, is this right and why? $$ \begin{matrix} 1 & * & *\\ 0 & 1 & *\\ 0 & 0 & 1 \end{matrix} $$

Let G be the free profinite group on 2 generators, $A=G/[G,[G,G]],B=G/[[G,G],[G,G]]$, then what is the structure of the groups $A$ and $B$?

I heard that $A$ is isomorphic to the group of such ($3\times 3$ below) matrices with entries in $\hat{\mathbb{Z}}$, is this right and why? $$ \begin{pmatrix} 1 & * & *\\ 0 & 1 & *\\ 0 & 0 & 1 \end{pmatrix} $$