How to determine if a language produced by grammar is recognizable by deterministic pushdown automaton (DPDA)?

I have a following grammar: S -> aSa | bSb | lambda.

And I have to figure out whether the language produced by this grammar is recognizable by DPDA. I can’t find any theoremas about it. Obviously, it’s a context-free language and can be recognized by DPA, but what about DPDA?