Mathematics: Commutative Group Theory versus Non-Commutative Group Theory

For any two Commutatives a and b of such a group, applying a and then b is the same as applying b and then a
this is where our so called multiplication of Commutatives or multiplication of numbers or Commutative transformations generically
when multiplying numbers, order doesn't matter
mathematically: a * b = b * a
analogy will help you understand this concept better: imagine that we are transforming the look of a person
let's say we have two transformations: a is putting on a shirt and b is putting on pant
if we apply a and then b, we get a person that wears shirt and pant
now let's apply these two transformations in the opposite order
we apply b and then we apply a and then we get the exact same result
so in this case, we say that a starred by b is the same as b starred by a

but let's now consider a slightly different pair of non-Commutative transformations
mathematically: (a - b) != (b - a)
analogy: a is putting on underwear and b is putting on pant
applying a and then b gives us roughly speaking a very conventional outcome
but applying transformation "b and then a" produces a noticeably different result like the old Superman movie

when operation order doesn't matter a group is called Commutative Group / Abelian Group
and guess what when the order does matter,
we call the group Non-Commutative Group / non-Abelian Group