Integer means a whole number , a number that is not fraction
Katie did not specifically said what numbers , the numbers can be fraction and it would not be called integer so that is Katie's error
(A) Product of
and
is:






(B) Yes.
Product of
and
= Product of
and
because multiplication is commutative.
Commutative Property of multiplication says that a.b = b.a.
Thus, multiplication is same irrespective of the order of two numbers.