Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 1F / b / Solution

Move the first $n-k$ columns ofpast its last $k$ columns. This requires $k(n-k)$ column interchanges and produces the block-diagonal matrixEach interchange reverses the determinant's sign, so part (a) gives

Solved by gpt-5.6-sol high.