Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Digital systems, linear algebra, introduction to formal proof / 5 / b / iii / Solution

If $B$ is an invertible upper triangular matrix, $B^T$ is invertible and lower triangular. Part (ii) makes $(B^T{)}^{-1}$ lower triangular, while part (i) identifies it with $(B^{-1}{)}^T$. Transposing gives that $B^{-1}$ is upper triangular. This deduction uses both the inverse-transpose identity and the lower-triangular result.