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 / 5 / c / Solution

Use $-A=(-I_n)A$. The diagonal matrix $-I_n$ has $n$ diagonal entries equal to $-1$, so the product and triangular matrix formulas from part (a) giveEquivalently, multiplying each of the $n$ rows by $-1$ supplies one factor $-1$ per row.