6. Consider the subring S = {[0], [2], [4], [6], [8], [10], [12], [14], [16] } C Z18 with respect to addition and multiplication defined in Z18, do the following questions. (a) Does S have the unity? (b) Does S have zero divisors? Which element of S have multiplicative inverses?

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A: We have to show that 13 divides 9a+8b To prove this we using 4a+5b divisible by 13

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A: Let V be all elements of R2 that have the form (a, a2) where a is a real number. We have show that…

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A: As asked we shall solve only question 2. (a).Let .(a) If gcd(a, m) = 1, then Bézout's lemma gives…

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Q: Compute: 3] 2 5-3

A: 1.a1a2a3a4+b1b2b3b4=a1+b1a2+b2a3+b3a4+b42. Two matrices can be added iff the order of the marices…

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A: Use the formula of zero divisors in Zm and the properties of Euler's Phi function as in next step.

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A: Given: A=23−1403  and  B=3−13124[AB](3,2)=?[AB](2,3)=?

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Q: 2 19) Find the value(s) of k such that A = [13] has an inverse. What is the inverse of A?

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Q: 2. Find the LU factorizations of and 20 5 2 -6 3 -13 -3 4 9 16 17 2 4 -6 2 13 9 دن و ان 5 4

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