Could I get some tips on describing this recursion language in English?

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I'm having a bit of trouble with this one. Here's the problem:

Basis : $a \in L$
Recursive definition : If $x \in L$, then $xb, xa$ and $bx$ are elements of $L$.

I get that strings which begin with a and end with b are in the language, and I also get that a set for the language would (roughly) appear as follows:

{a, ab, aa, ba, aab, aaa, baa, aaab, aaaa, baaa, …}

But I'm having issues with bringing this to a conclusive statement. Please help. Would something like, "all strings within this language begin and end with either b or a" work, or is that too simple?

I hope all of this is clear, and that I haven't made any mistakes with what I have so far.