prove -x - y = - y - x, for all integers x and y and does part (a) imply that subtraction is commutative

Answer 1

we know that
addition is commutative
multiplication is distributive over addition

so,

-x-y = -(x+y) = -(y+x) = -y-x

subtraction is not commutative, since

x-y = -(y-x) = -y+x
a single counterexample sufficeth:

3-4 = -1
4-3 = +1