8. Let S be the set of all 2 x 2 matrices of the form where x is an integer. Assume that S is a ring with respect to matrix addition and multiplication. (a) Is S a commutative ring? (b) Does S have a unity? (c) Does S have zero divisors?

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Q: 10. Decompose x* + 4.x² + 1 into a product of irreducible polynomials in the following rings: (a)…

A: To find - Decompose x4 + 4x2 + 1 into a product of irreducible polynomials in the following rings :…

Q: Enter the multiplicative inverse of the element [21]49 X+ [18]49 in the ring Z49[x].

A: Extended Euclidean Algorithm

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A: It is impossible.

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Q: 9. Which of the following statements refutes the claim that GLR(3), the set of 3 x 3 invertible…

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A: A, B, C are coplanar.So

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