Has anyone ever seen a first of A.S. Byatt's 'Elementals'?

I have a copy which has her signature on the title page. But the signature appears to be exactly the same colour as the ink used to print the book. I can see no impression made by a pen, either on the reverse of the page or by holding it at an angle to a light source.

Is this a printed facsimile?

I've looked around and some are claimed to be signed, but does that mean that it is signed in addition to the facsimile (if that is what it is) or are others just assuming?

If anyone has a copy of the first impression without a signature on the title page please let me know.

. ------------------------------------------------------------------------------------------------------------------------------------------------------Whomever you may murder, there's no police like Holmes.
Σ Ψ Δ
σ ψ δ
------------------------------------------------------------------------------------------------------------------------------------------------------Whomever you may murder, there's no police like Holmes.
Σ Ψ Δ
σ ψ δ