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: ​

2 apples

step-by-step explanation:

taking away equals subtraction. 6-4=2

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)