 Solution

ID: 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

- I_{n}

has

n

diagonal entries equal to

- 1

, so the product and triangular matrix formulas from part (a) give

det (- A) = det (- I_{n}) det (A) = (- 1)^{n} det (A) .

Equivalently, multiplying each of the

n

rows by

- 1

supplies one factor

- 1

per row.

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