if PEDMAS is a law

It isn't, it's a convention. Not sure how many times you need to be told that 🙄

THANK YOU. this is what I've been trying to tell you the entire fucking time. PEMDAS is not a law, its a convention.

but just in case you decide to go back on that, and since you seem to be obsessed with the idea that all notations adhere to PEMDAS - let me blow your mind:

here is the distributive law, written in the 3 notations we've been talking about:
prefix: *a+bc = +*ab*ac
infix: a(b+c) = ab+ac
postfix: abc+* = ab*ac*+

(not using juxtaposition multiplication for prefix/postfix for clarity)

so where does PEDMAS get involved in prefix or postfix notations?

regarding your textbook being the first google result... are you referring to the textbook from 1913? for someone talking about the importance of textbooks, thats a really strange choice. I can't find another with the same name and author of either Coll or Rich.
and hilariously, if you look at that text book, on page 90 it says the following:

Probably the most common error consists in breaking the laws of precedence of operations (§ 13). These laws were made arbitrarily, but are recognized the world over, and the student must accept and memorize them.