I know that the BEDMAS rules (Brackets - Exponents - Division OR Multiplications - Addition OR Subtraction) for Order of Operations apply to scalars and algebraic expressions.
Do the BEDMAS rules for Order of Operations apply to other "Mathematical Objects", such as Matrices or Vectors? (I am in high school, so I am not sure if there are any other types of "mathematical objects")
For instance, do the BEDMAS rules apply for the following expression with matrices:
$5A+3B$
Where in this case the scalar multiplication would be evaluated first, followed by Addition So that $5A+3B = (5A) + (3B)$ ,
What about a case involving matrix multiplication:
$A × B + C × D$
Would Matrix Multiplication be computed first, followed by Addition?
Such that: $ A × B + C × D = (A × B) + (C × D) $
Or in the case involving cross product of vectors? Would the cross product operation be interpreted as a multiplication operation and take precedence over addition?
Eg. $ u × v + w = (u × v) + w $ instead of: $ u × v + w = u × (v + w)$
I know this seems like a very straightforward question, and it would make sense that the BEDMAS rules would also apply to other mathematical objects. However, since this is not explicitly taught I want to make sure.