Sarrus

The Rule of Sarrus is a mnemonic device for calculating the determinant of a 3 × 3 matrix. It is named after the French mathematician Pierre Frédéric Sarrus.

To apply the Rule of Sarrus, the 3 × 3 matrix is augmented by repeating the first two columns to the right of the matrix. Then, the determinant is the sum of the products of the elements along the three diagonals running from upper-left to lower-right, minus the sum of the products of the elements along the three diagonals running from upper-right to lower-left.

More formally, given a 3 × 3 matrix:

A = | a  b  c |
    | d  e  f |
    | g  h  i |

The determinant of A, denoted as det(A) or |A|, can be calculated as:

det(A) = aei + bfg + cdh - ceg - afh - bdi

The Rule of Sarrus offers a straightforward method for hand calculation of 3x3 determinants, though it does not generalize to larger matrices. For matrices larger than 3x3, other methods such as cofactor expansion or Gaussian elimination are typically used to compute the determinant.