can you disprove this rule PEDMSA?-(division before multiplication, subtraction before addition) I know the proper teaching of PEMDAS/PEDMAS/BODMAS/BOMDAS..  is that multiplication and division have equal priority and are evaluated going through the arithmetic expression left to right (So, doing division first if division is left of multiplication in the arithmetic expression, and multiplication first if it is to the left of a division). Ditto for addition and subtraction.

And I know PEMDAS if taken as multiplication always before division, gives wrong answers. And addition always before subtraction, also gives wrong answers. e.g. 3-2+1 addition before subtraction would be wrong result.  And 6/2*3 multiplication before division would be wrong result.

So one can break(get a wrong result from), a literal reading of PEMDAS, i.e. doing multiplication always before division, and ditto with additionan and subtraction.

But how about a literal reading of   PEDMSA?   so, taking it literally..  division always before multiplication.  Subtraction always before addition.  

Can you break it(get a wrong result from it)?
This question brings to light an excellent example of how we can introduce ambiguity into a language by removing one interpreter rule from a language/interpreter system. 

A language and the corresponding interpreter go hand in hand. When we construct a language, and the corresponding interpretation rules, the onus is on the writer to phrase statements in a way that will always give the desired result by the corresponding interpreter. While there may be many speakers of one language, there is only one interpreter for languages of this sort.

Polish notation would be an example of an alternative language for arithmetic operations. 

As you know, the "PEMDAS" rule is nothing more than a mnemonic device to assist in interpreting what is currently our most common language for operation order. The left to right scanner priority rule is however an integral part of this device, and PEMDAS would be best written as $P-E-(M \vee D)-(A\vee S)$ "with repeated left to right scan priority after each atomic operation execution".

We can make a new language and interpreter at will. We can also modify a language, but once you decide to modify an extant language/interpreter, like say "remove the left to right rule", then all bets are off. You now have a new language, it is not the old language, and things may need to either be written differently or interpreted differently for this new language, otherwise there will be problems, ambiguity being one such problem. 

If you modify the language, you probably need to modify the interpreter. If you modify the interpreter, you probably need to modify the language.
Most of this is above my head, but I take issue with the OP that 3-2+1 cannot be done with addition before subtraction.

Subtraction is just adding a negative number, so that calculation is actually (+)3+(-2)+1

No matter what order you do that on your going to get the same result.

3+(-2)+1 = 2

3+1+(-2) = 2

(-2)+3+1 = 2

(-2)+1+3 = 2

1+(-2)+3 = 2

1+3+(-2) = 2

Multiplication is just repetitive addition, 

8×3 = 3+3+3+3+3+3+3+3

Division is inverse multiplication so 

8÷3 = 8×⅓ = ⅓+⅓+⅓+⅓+⅓+⅓+⅓+⅓

Now division before multiplication is more difficult.

6÷2×3

This is either

(6÷2)×3 =

(6×½)×3 =

(½+½+½+½+½+½) + (½+½+½+½+½+½) + (½+½+½+½+½+½) = 

3+3+3 = 9

Or it is

6÷(2×3) = 

6÷6 = 6×⅙ = 

⅙+⅙+⅙+⅙+⅙+⅙ = 1

In that example, the division it written first, so reading left to right it would be done first, and the answer should be 9

But what if the equation was written the other way around?

3×6÷2 ???

LTR

(3×6)÷2 = 

18÷2 =

18 × ½ =

½+½+½+½+½+½+½+½+½+½+½+½+½+½+½+½+½+½ = 9

DBM

3×(6÷2) =

3×(6×½) =

(½+½+½+½+½+½) + (½+½+½+½+½+½) + (½+½+½+½+½+½) =

3+3+3 = 9

So interestingly, in the latter calculation the order made no difference, but in the former, it made a huge difference.

I can't actually say, based on above that DBM will always yield the incorrect result!