Upper triangular matrices have determinant equal to their diagonal product. Row replacement preserves determinant and a row swap reverses its sign. Therefore elimination without row scaling gives $\det A=(-1)^s\prod_i u_{ii}$. Ignoring the swap sign is a common error. For pivoted LU, this is also $\det A=\det(P)\prod_i u_{ii}$ when $L$ is unit triangular and $PA=LU$.
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.