>what are some scenarios that prove PEMDAS to be the absolute truth
It’s not. There is ambiguity in PEMDAS and as such you will notice that parenthesises are heavily utilized in university (higher) level math to avoid any possible ambiguity.
PEMDAS is mostly good enough and works by convention. The goal of order of operations is to make sure that everyone gets the same results.
But without properly using brackets you might find different calculators will give you different results due to this ambiguity.
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