Is There a Mistake in My Proof for the Identity of Pauli Spin Matrices?

[InGaAsP]

Homework Statement

prove the idendity \sigma \times \sigma =i \sigma where \sigma is Pauli Spin matrices

Homework Equations

The Attempt at a Solution

This is how I did..and I am getting
2i \sigma instead of i\sigma.

http://i146.photobucket.com/albums/r273/soorajr/paulimatrix.jpg

This question was asked twice for the university exam, and during both times, they asked us to prove \sigma \times \sigma =i \sigma.
Did i make any mistake? or the examiner was wrong?
Thanks in advance.

 

[Galileo]

You wrote (for instance) \sigma_y\sigma_z-\sigma_z\sigma_y=i\sigma_x
but then later when you get the same expression for the x-component you enter
i\sigma_x+i\sigma_x, which is where your factor 2 comes from.
Check the middle line in your calculation of the determinant again

 

[InGaAsP]

You wrote (for instance) \sigma_y\sigma_z-\sigma_z\sigma_y=i\sigma_x
but then later when you get the same expression for the x-component you enter
i\sigma_x+i\sigma_x, which is where your factor 2 comes from.
Check the middle line in your calculation of the determinant again

Thanks Galileo for ur reply

the results i used were\sigma_x\sigma_y=-\sigma_y\sigma_x=i\sigma_z
i changed x,y,z cyclicly, and hence reached at 2i \sigma
do u think I am supposed to get only i\sigma instead of 2i\sigma
thanks in advance

 

[nrqed]

Homework Statement

prove the idendity \sigma \times \sigma =i \sigma where \sigma is Pauli Spin matrices

Homework Equations

The Attempt at a Solution

This is how I did..and I am getting
2i \sigma instead of i\sigma.

http://i146.photobucket.com/albums/r273/soorajr/paulimatrix.jpg

This question was asked twice for the university exam, and during both times, they asked us to prove \sigma \times \sigma =i \sigma.
Did i make any mistake? or the examiner was wrong?
Thanks in advance.

Yes, there is a mistake in the question. There really should be a factor fo 2 there.

 

[Galileo]

Indeed, your first lines should be \sigma_y\sigma_z-\sigma_z\sigma_y=2i\sigma_x etc.