True/false: negative numbers closed under subtraction. provide an example if false

Consider a set M, and an operation *.

Let a and b be in M, then M is closed under operation * if :

a*b, and b*a produce an element of M


The set of negative numbers (set M) is not closed under subtraction (the operation *).

Consider 2 numbers a=-9 and b=-6 which certainly are in M.

-9*(-6) = -9-(-6)=-9+6=-3 ∈ M   (note that * is the regular subtraction -)

(-6)*(-9)=-6-(-9)=-6+9=3 ∉ M