##6/2(1+2) =\ 6/2(3) =\ 6/6 =\ 1##
##\frac{6}{2(1+2)} =\ \frac{6}{2(3)} =\ \frac{6}{6} =\ 1##

This is due to how their division works. It's a fraction, not the ÷ symbol. So its 6 over 2(1+2) not six divided by 2(1+2). The way that TI-OS does it there is wrong according to that.

##6÷2(1+2) =\ 6÷2(3) =\ 3(3) =\ 9##

If we aren't treating it as a fraction then it is correc according to standard order of operations.

TI calculators interpret this just like any other interpreter or compiler would, it's CASIO that is wrong here. It's the only way that makes sense without natural expression display. The only difference is that the * operator is implicit.

This is how Python 3 does it:
>>> 6/2*(1+2)
9.0

When in doubt add more parentheses to eliminate the ambiguity.