Does this table show a binary operation

1

• Does this table show a binary operation?
• Yes
• No

2

• Is there an identity element? If so, what is it?
• No (b) Yes, p
• Yes, q (d) Yes, r
• (e) Yes, s (f) Yes, t
• (g) Yes, u (h) Yes, v
• (i) Yes, w

3

• Does p have an inverse?
• If so, what is it?
• No (b) Yes, p
• Yes, q (d) Yes, r
• (e) Yes, s (f) Yes, t
• (g) Yes, u (h) Yes, v
• (i) Yes, w

4

• Does q have an inverse?
• If so, what is it?
• No (b) Yes, p
• Yes, q (d) Yes, r
• (e) Yes, s (f) Yes, t
• (g) Yes, u (h) Yes, v
• (i) Yes, w

5

• Does every element have an inverse?
• Yes
• No

6

• Does this table define a group?
• Yes
• No
• I dont know and if you think I am going to
  check associative you are out of your freaking
  mind.

7

• What is the order of this group?
• 1 (b) 6
• 8 (d) 50
• (e) 64 (f) Primary

8

• Is this group abelian?
• Yes
• No