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

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 $\det A=\det L\det U=6$.