Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof / 3 / d / Solution

The elementary row operations used above add multiples of other rows, so preserve the determinant. The determinant of an upper triangular matrix is the product of its diagonal entries. HenceEquivalently, $\det L=1$ and multiplicativity of the determinant gives $\det A=\det L\det U=6$.