Group Definition                    QUIZ 2.1

1. The positive integers are closed under subtraction. (a) T
(b) F
     
2. The non-zero real integers are associative under division. (a) T
(b) F
     
3. The inverse of 3 under addition
(a) is 1/3, (b) is –3, (c) does not exist.		 (a)
(b)
(c)
     
4. The integers are commutative under subtraction. (a) T
(b) F
     
5.  The set of 2 x 2 matrices forms a group under matrix multiplication. (a) T
(b) F
     
 6. The set of 2 x 2 matrices forms an abelian group under matrix addition. (a) T
(b) F
Check answers
1. (b) For example, 2 – 3 is not a positive integer.


2. (b) For example, (12 / 6) / 2 = 1, but 12 / (6 / 2) = 4.


3. (b) 3 + (–3) = 0, which is the additive identity.



4. (b) For example, 4 – 2 = 2,
but 2 – 4 = –2.

5. (b) The set of 2 x 2 non-singular matrices forms a group under matrix multiplication.

6. (a) The five axioms are satisfied in this case.