Unrelativised standard commutator formula

In the present note, which is a marginalia to the previous papers by Roozbeh Hazrat, Alexei Stepanov, Zuhong Zhang, and the author, I observe that for any ideals $A,B\unlhd R$ of a commutative ring $R$ and all $n\ge3$ the birelative standard commutator formula also holds in the unrelativised form, as $[E(n,A),\mathrm{GL}(n,B)]=[E(n,A),E(n,B)]$ and discuss some obvious corollaries thereof.