# How do you find the determinant of |(4,6,7),(3,-2,-4), (1,1,1)|?

Aug 3, 2017

The Rule of Sarrus! -> $\det \left(A\right) = 1$

#### Explanation:

Order three determinants follow The Rule of Sarrus . Consider a matrix

$A = | \left({a}_{1} , {a}_{2} , {a}_{3}\right) , \left({a}_{4} , {a}_{5} , {a}_{6}\right) , \left({a}_{7} , {a}_{8} , {a}_{9}\right) |$

The Rule of Sarrus says:

$\det \left(A\right) = | A | = {a}_{1} {a}_{5} {a}_{9} + {a}_{2} {a}_{6} {a}_{7} + {a}_{3} {a}_{4} {a}_{8} - {a}_{3} {a}_{5} {a}_{7} - {a}_{6} {a}_{8} {a}_{1} - {a}_{9} {a}_{4} {a}_{2}$

These pictures may help in understanding what this rule does:

Positive sign:

Negative sign:

$| A | = - 8 - 24 + 21 + 14 + 16 - 18 = 1$