If given a n*n matrix with all rows and columns sum to 0, how do I argue that all its (n-1)*(n-1) minor have the same determinant up to a sign?(adsbygoogle = window.adsbygoogle || []).push({});

Since all rows and columns all sum to 0, then I know that any column is a linear combination of all others, so that the determinant of this n*n matrix must be zero, then since the determinant is calculated using minors, it seems to imply that all (n-1)*(n-1) minors must have the same determinant up to a sign, but how do I rigorously prove that?

**Physics Forums - The Fusion of Science and Community**

# Determinant of minor

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

Have something to add?

- Similar discussions for: Determinant of minor

Loading...

**Physics Forums - The Fusion of Science and Community**