A. Let ⋆ be the binary operation on Z (set of integers) defined by a ⋆ b = 2ab + 5
1. Show that ⋆ is commutative. Hint: Show that a ⋆ b = b ⋆ a
Solution:

2. Show that ⋆ is associative. Hint: Show that (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c)
Solution:

B. Let ⋆ be the binary operation on Z (set of integers) defined by
a ⋆ b = a + b + ab
1. Show that ⋆ is commutative. Hint: Show that a ⋆ b = b ⋆ a
Solution:

2.Show that ⋆ is associative. Hint: Show that (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c)
Solution: ​