let $L: \mathbb R^2\to\mathbb R^2$ be a linear operator which is invertible. Let {$u, v$} be a linearly independent set in $\mathbb R^2$. Find a formula for the area of the parallelogram induced by $L(u)$ and $L(v)$ in terms of the area of the parallelogram induced by $u$ and $v$.
So I'm trying to find det($L(u)$,$L(v)$) since this is the area. Not sure on how to do this problem.