It's embarrassing to say, but I didn't realise the 12 Zodiacs corresponded directly to the houses, as you've said.
Initially, I thought the response would be "No", as it isn't explicitly stated here (link below), as it is for Venus (2nd and 7th).
https://www.joyofsatan.org/www.angelfire.com/empire/serpentis666/PlanetMercury.html
I had all these wild ideas about what may be the reason, hence the post to clear my confusion.
Does this mean a sign's element relates to the house? Such as Aries (Mars) ruling the 1st, thus its element is Fire?
Thank you also to Blackdragon666 and Bright Truth for responding, I appreciate it.