Solution
= Solution
$A=\mathbb Z^2/\langle(6,9)\rangle$. The class of $(2,3)$ has order $3$, so $A$ has torsion and is not free. A unimodular change of <basis> (<Smith normal form>, using $\gcd(6,9)=3$) gives $A\cong\mathbb Z\oplus\mathbb Z/3\mathbb Z$.