It's important to use PEMDAS to solve problems, to ensure that everyone solves a problem the same way. If I wanted to demonstrate how to do a problem, but used a different order of operations, I would get a different answer than everyone else. That wouldn't make me wrong, just different, which, in math, is unnecessary. Math has either a right or wrong, so if people got multiple answers for a problem that was supposed to only have 1, it would cause confusion. Additionally, when doing proofs, one needs to be able to reconstruct a scenario created. If PEMDAS didn't exist, then you wouldn't be able to always accurately reconstruct a scenario in math.
