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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Q. Minimum subgroup of a group is called _____________

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Q. Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the size of H is at least 3. The size of H is __________

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Q. __________ is not necessarily a property of a Group.

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Q. A group of rational numbers is an example of __________

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Q. Intersection of subgroups is a ___________

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Q. The group of matrices with determinant _________ is a subgroup of the group of invertible matrices under multiplication.

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Q. What is a circle group?

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Q. A normal subgroup is ____________

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Q. Two groups are isomorphic if and only if __________ is existed between them.

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Q. a * H is a set of _____ coset.

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Q. a * H = H * a relation holds if __________

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Q. Lagrange’s theorem specifies __________

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Q. A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called _____________

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