Pauli matrices and the Levi-Civita tensor : commutation relations

[Dixanadu]

Homework Statement

Whats up guys!

I've got this question typed up in Word cos I reckon its faster:
http://imageshack.com/a/img5/2286/br30.jpg

Homework Equations

I don't know of any

The Attempt at a Solution

I don't know where to start! can u guys help me out please?

Thanks!

 

[nejibanana]

You can start by multiplying each possible combination of pauli matrices. Do that and factor out a 1 or -1, which can be replaced with a Levi-Cevita symbol. Use i = 1, j = 2, k = 3.

 

[Dick]

Sure, just check it by putting the matrices into the commutation relation. For example, show $[\sigma_1,\sigma_2]=\sigma_1 \sigma_2-\sigma_2 \sigma_1=i\sigma_3$. But it's not going work very well until you fix $\sigma_3$. That's not a Pauli matrix.