Let See Exercise 48 in Chapter 2 for the definition of
Chapter 8, Problem 38E(choose chapter or problem)
Let
\(H=\left\{\left[\begin{array}{lll}1 & a & b \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right] \mid a, b \in Z_{3}\right\}\)
(See Exercise 48 in Chapter 2 for the definition of multiplication.) Show that H is an Abelian group of order 9. Is H isomorphic to \(Z_{9}\) or to \(Z_{3} \oplus Z_{3}\)?
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