this is a homework question but I am pretty confused on it--just don't know where to start.
We're given a lattice basis $(a, b)$ for a lattice $L$ in $\mathbb{R}^2$, and are supposed to show that every other lattice basis (a', b') can be written as $(a, b)P$ for some $2\times 2$ integer matrix $P$ with determinant $\pm 1$.