TITLE: Sarrus determinant rule: references, extensions
QUESTION [7 upvotes]: 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

REPLY [2 votes]: I've posted a diagram version of 4x4 Sarrus here: http://www.theoremoftheday.org/GeometryAndTrigonometry/Sarrus/Sarrus4x4.pdf