Discrete Maths - Sets

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31. If (G, .) is a group, such that (ab)² =a²b² ∀ a, b ∈ G, then G is a/an

Answer
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Array

Option : B
Explanation :

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32. (Z,*) is a group with a*b = a+b+1 ∀ a,b ∈ Z. The inverse of a is

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Option : D
Explanation :

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33. Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an

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Option : C
Explanation :

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34. Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then

A
A is closed under * but is not a semi group
B
is a semi group but not a monoid
C
is a monoid but not a group
D
is a group but not an abelian group

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Option : D
Explanation :

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35. If a, b are positive integers, define a * b = α where ab = α (modulo 7), with this * operation, then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is

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Option : C
Explanation :

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