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Recall that we write F5 for the field consisting of congruence classes modulo 5. The elementsof this field are usually denoted by 0, 1, 2, 3 and 4, and the addition and multiplicationare computed modulo 5. Consider the following set of matrices G=\left\{\left(\begin{array}{ccc}

1 & a & b \\

0 & 1 & c \\

0 & 0 & 1

\end{array}\right) \mid a, b, c \in \mathbb{F}_{5}\right\} (a) Show that matrix multiplication defines a binary operation on the set G. (b) Show that G is a group with respect to matrix multiplication. (c) Determine whether or not this group G is abelian.

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