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## Homework Statement

show that the determinant of a matrix A can be calculated as followings:

det[A]= 1/6 (A_ii A_jj A_kk + 2 A_ij A_jk A_ki - 3 A_ij A_ji A_kk

## Homework Equations

## The Attempt at a Solution

use ε_pqr det[A]= ε_ijk A_ip A_jq A_kr

ε_pqr ε_pqr det[A]= ε_ijk ε_pqr A_ip A_jq A_kr

use ε_pqr ε_pqr = 6

det[A]= 1/6 ( ε_ijk ε_pqr A_ip A_jq A_kr)

and ε_ijk ε_pqr = det | δ_ip δ_iq δ_ir |

| δ_jp δ_jq δ_jr |

| δ_kp δ_kq δ_kr |

from here i dont know what to do

and δ - delta and ε - epsilon