Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 5 / d

The determinant of the unit lower triangular matrix $L$ is 1. There is one row swap, so $\det P=-1$, and the upper triangular matrix has determinant $1\cdot (-2)\cdot (3/2)\cdot 2=-6$. Therefore