math
posted by olivia on .
prove xy=yx, for all integers

I do not know what grade you're in, but questions of this sort could go quite deep into algebra.
Since x,y are integers, which belong to a ring in which additions are commutative, so if we write the subtractions as inverses of addition, the above would be invoking commutativity in the ringaddition:
xy
=(x)+(y) inverse of addition
=(y)+(x) commutativity of addition
=yx inverse of addition
For highschool algebra, then it would be the commutative property of addition and subtraction.