Are there Exceptions to the commutative property?

Answer 1

The commutative property works for adding and multiplying e.g. 2+4=4+2 and 3x4=4x3.

But it doesn't work for subtraction and division so 5-3≠3-5 and 6÷2≠2÷6 so subtraction and division could be considered as exceptions.

Answer 2

Depending what exactly you mean...* The commutative property for addition (or for multiplication) with real numbers always applies - NO EXCEPTIONS.

* In math, there are operations known as "multiplication" which share some characteristics with the common multiplication, but for which the commutative property usually does NOT apply. For example, cross-multiplication of vectors, or multiplication of matrices. In the case of matrices, it's even possible that A x B is defined, whereas B x A is not defined (because the matrices are of incompatible sizes). For two square matrices, both A x B and B x A are defined, but the results may be quite different.