(a) State the classification theorem for finitely generated modules over a Euclidean domain.

(b) Deduce the existence of the rational canonical form for an $n \times n$ matrix $A$ over a field $F$.

(c) Compute the rational canonical form of the matrix

$$A=\left(\begin{array}{ccc} 3 / 2 & 1 & 0 \\ -1 & -1 / 2 & 0 \\ 2 & 2 & 1 / 2 \end{array}\right)$$