Linear Algebra
Sarrus rule for a 3 by 3 matrix
Three down-right diagonal products minus three down-left ones. Only valid for 3 by 3.
The Formula
det = aei + bfg + cdh - ceg - bdi - afh
Three down-right diagonal products minus three down-left ones. Only valid for 3 by 3.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a ... i | Matrix entries | unitless | The nine entries read row by row. |
| aei + bfg + cdh | Down-right terms | unitless | The three diagonals running down to the right. |
| ceg + bdi + afh | Down-left terms | unitless | The three diagonals running down to the left. |
What Each Symbol Means
a ... iunitless
Matrix entries
The nine entries read row by row.
aei + bfg + cdhunitless
Down-right terms
The three diagonals running down to the right.
ceg + bdi + afhunitless
Down-left terms
The three diagonals running down to the left.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a matrix determinant page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Matrix Determinant, filed under Math. Every number the guide produces comes from substituting into this one line.