Rule of Sarrus
Consider a 3×3 matrix
then its determinant can be computed by the following scheme:
Write out the first 2 columns of the matrix to the right of the 3rd column, so that you have 5 columns in a row. Then add the products of the diagonals going from top to bottom (solid) and subtract the products of the diagonals going from bottom to top (dashed). This yields:
A similar scheme based on diagonals works for 2×2 matrices:
Both are special cases of the Leibniz formula, which however does not yield similar memorization schemes for larger matrices. Sarrus's rule can also be derived by looking at the Laplace expansion of a 3×3 matrix.
Another way of thinking of this is to imagine that the matrix is wrapped around a cylinder, such that the right and left edges are joined.
- Paul Cohn: Elements of Linear Algebra. CRC Press, 1994, ISBN 9780412552809, p. 69
- Khattar, Dinesh (2010). The Pearson Guide to Complete Mathematics for AIEEE (3rd ed.). Pearson Education India. p. 6-2. ISBN 978-81-317-2126-1.
- Fischer, Gerd (1985). Analytische Geometrie (in German) (4th ed.). Wiesbaden: Vieweg. p. 145. ISBN 3-528-37235-4.