Q. A relation (34 × 78) × 57 = 57 × (78 × 34) can have __________ property.

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Q. B₁: ({0, 1, 2….(n-1)}, xₘ) where xₘ stands for “multiplication-modulo-n” and B₂: ({0, 1, 2….n}, xₙ) where xₙ stands for “multiplication-modulo-m” are the two statements. Both B₁ and B₂ are considered to be __________

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Q. If group G has 65 elements and it has two subgroups namely K and L with order 14 and 30. What can be order of K intersection L?

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Q. Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of _______

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Q. Let * be the binary operation on the rational number given by a*b=a+b+ab. Which of the following property does not exist for the group?

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Q. Let G be a finite group with two sub groups M & N such that |M|=56 and |N|=123. Determine the value of |M⋂N|.

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Q. A group G, ({0}, +) under addition operation satisfies which of the following properties?

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Q. If (M, *) is a cyclic group of order 73, then number of generator of G is equal to ______

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Q. The set of even natural numbers, {6, 8, 10, 12,..,} is closed under addition operation. Which of the following properties will it satisfy?

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Q. In a group there must be only __________ element.

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Q. _____ is the multiplicative identity of natural numbers.

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Q. An identity element of a group has ______ element.

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Q. __________ matrices do not have multiplicative inverses.

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Q. If X is an idempotent nonsingular matrix, then X must be ___________

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Q. If A, B, and C are invertible matrices, the expression (AB⁻¹)⁻¹(CA⁻¹)⁻¹C2 evaluates to ____________

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Q. If the sum of elements in each row of an n×n matrix Z is zero, then the matrix is ______________

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Q. ___________ are the symmetry groups used in the Standard model.

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Q. A semigroup S under binary operation * that has an identity is called __________

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Q. An element a in a monoid is called an idempotent if ______________

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Q. A trivial subgroup consists of ___________

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