3x3 Determinant

We can solve a 3x3 determinant by applying the following formula:

Determinant of Order Three=

a11 a22 a33 + a12 a23 a 31 + a13 a21 a32 -

- a 13 a22 a31 - a12 a21 a 33 - a11 a23 a32.

Since this formula is difficult to memorize, the rule of Sarrus is used to solve 3x3 determinants.


Rule of Sarrus

The terms with a + sign are formed by the elements of the principal diagonal and those of the parallel diagonals with its corresponding opposite vertex.

Positive Rule of Sarrus


The terms with a sign are formed by the elements of the secondary diagonal and those of the parallel diagonals with its corresponding opposite vertex.

Negative Rule of Sarrus


Example

Rule of Sarrus