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Which of the following is true?

  1. The set of all rational negative numbers forms a group under multiplication.
  2. The set of all non-singular matrices forms a group under multiplication.
  3. The set of all matrices forms a group under multiplication.
  4. Both B and C are true.

4 Answers

Best answer
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Answer: B

  1. False. Multiplication of two negative rational numbers give positive number. So, closure property is not satisfied.
  2. True. Matrices have to be non-singular (determinant $\neq0$) for the inverse to exist.
  3. False. Singular matrices do not form a group under multiplication.
  4. False as C is false.
edited by
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Option b
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  1. If a relation is group then it must be

1)Closed

2)Associative

3)Identity

4)Inverse

if a matrix is non-singular then inverse dose not exist. So option c is wrong.

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(a) False, because 0 does not have an inverse

(b) True, Non-singular means Determinant!=0 So it is a group

(C) False, Determinant of the matrix can be zero which does not have an identity so not a group

(D) False
Answer:

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