Will the dextrorotatory and laevorotatory enantiomers always have a set of stereocenters with opposite absolute configuration?
Precisely, these are based on the configurations proposed by German chemist Emil Fischer, who established the structures of many sugars.


  Emil Fischer elucidated these configurations for the aldohexoses in
  1896. According to the Fischer convention, D sugars have the same absolute configuration at the asymmetric center farthest removed from
  their carbonyl group as does D-glyceraldehyde. The L sugars, in
  accordance with this convention, are mirror images of their D
  counterparts,




Similary,the  Fischer projection for glucose  is shown below.



It is very important not to confuse these enantiomers with epimers   (two sugars that differ only in the configuration around one carbon atom e.g D-glucose and D-mannose, which differ only in
the stereochemistry at C-2)



References


Voet and Voet Biochemistry
Lehninnger Principles of Biochemistry
Biochemistry (Campbell and Farrel)