Possibly. We don't know whether it is being fed with AC or DC (clearly not 230V, as some people 'assumed' ). If it's DC, "doesn't matter" would only be true if the design includes a diode bridge - if it doesn't, then its LEDs wouldn't work with 'wrong polarity' DC.
Well yes, of course. If the light wants 12V and you connect it directly to 230V mains electricity, you'll get (at least) a bang and, maybe a flash, and that will be the end of it (but hopefully not of you). I would have expected a reputable seller to have at least offered (for a price), if not included, a suitable power supply for it.
Probably best not to have got the mains adapter from the same seller.
I have a lurking suspicion that the 2012-Olympic-opening-ceremony-stylee lighting effects on the seller's page might not actually have been achieved with the unit offered for sale.
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