SEEKING REFERENCES FOR SARRUS' RULE AND EXTENSIONS 


An undergraduate came to me with an identity for 4x4 determinants that is actually correct:


$\det(A)=h(A)+h(RA)+h(R^{2}A)$ 


where R cyclically permutes the last three rows of the matrix A. I wont define h here but, except for the signs of the terms, it is the usual incorrect extension of Sarrus Rule that is familiar to anyone who has has taught linear algebra (His identity is not the Laplace expansion, as it has three 4x4 matrices, rather than four 3x3 matrices. )


Is something like this known? Mathscinet lists a paper Monaco and Monaco that might be relevant, but my library couldnt get it. I haven't even found the original reference for Sarrus' rule itself.


Eric Schmutz



Sarrus determinant rule: references, extensions
I have found references to the Sarrus determinant rule and to an extension of it. In The Quarterly journal of pure and applied mathematics, Volume 38 which is available on Google books in the article "A fourth list of writings on determinants". On page 239 There is a reference to what I believe is Sarrus original result. Then on page 350 there is a reference to an extension of Sarrus' original result. I believe that part one of Muir's book on determinants and their history is available on Google books


