part A
The given group with an operation of subtraction does not satisfy the first conditions( did not even consider the other ones, as Closure is not satisfied). For all elements a and b in the group, the element a*b is also in the group.
Let a = 3 and b = 5, but then 3-5=-2 which is not a natural number, and is not in the group, therefore it is not a group
part B
This group does not satisfy ASSOCIATIVITY. Let a = 2 b = 4 c = 6, then (a*b)*c = (b*c)*a ( 48 = 48), but when division comes in, this condition is not satisfied, eg : ((a/b))/c ( 1/12) is not equal to ((b/c))/a ( 1/3) and therefore it is not a group
part C
This groupd is not closed in a different sense. if a and b are in the groupd then a*b is in the group too. But what if a and b both are negative and since are not part of the original group? -*- is a + and it would become part of the group
part D
It is a similar problem with this group. even*even always = even, but even*odd can equal even, and therefore non-members of the original group could become part of the group, and therefore the group is not closed.
part E
The only identity element of an addition group can only be 0 therefore it is 0.
as a"*a = a*a" = e and e is equal to 0, the inverse of this group would be -m, but in this case its 0 as e = 0
part F
it is an exponential and the only identity can be 1 and the inverse would still be 1 and whatever you do, whatever power you raise it to or decrease it , it will always be 1
Part G
It has to be 1 due to the multiplication, otherwise it would 0. and for inverse, it is still 0.