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Sarrus Rule


The calculation of the 3rd order determinant can be done by means of a practical device called Sarrus's rule.

Follow how we apply this rule to .

1st step: We repeat the first two columns next to the third:

2nd step: We find the sum of the product of the elements of main diagonal with the two products obtained by multiplying the elements of the parallel to this diagonal (the sum must be preceded by the plus sign):

3rd step: We find the sum of the product of the elements of secondary diagonal with the two products obtained by multiplying the elements of the parallel to this diagonal (the sum must be preceded by the negative sign):

Like this:

Note: If we develop this 3rd order determinant by applying the Laplace Theorem, we will find the same real number.

Order determinant n> 3

We have seen that the Sarrus rule is valid for the calculation of the determinant of an order 3 matrix. When the matrix is ​​of order greater than 3, we must employ Laplace's theorem to arrive at order 3 determinants and then apply the Sarrus rule. .

Next: Determinant Properties