Understand Vector Product with Levi Civita Symbols

[Septim]

Hello I am a graduate student and it is my first year in physics. Our instructor showed vector product with Levi Civita symbol and I did not understand the part where the product of two Levi Civita symbols is expressed as Kronecker Deltas. Additionally I did not get the proof on the URL http://folk.uio.no/patricg/teaching/a112/levi-civita/ can you explain these. Thanks for your contribution.

 

[vishal007win]

now take dot product of two vector products
(aXb).(cXd), which can be expressed further as
(aXb).(cXd)=c.((d.b)a - (d.a)b)

plug in the values of vector product using above equation(which includes levi civita symbols)
and then finally this would lead to the expression