# Help about Pauli spin matrix

## Homework Statement

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

## The Attempt at a Solution

This is how I did..and I am getting
2$$i \sigma$$ 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?

Last edited:

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Galileo
Homework Helper
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

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

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 2$$i \sigma$$
do u think I am supposed to get only i$$\sigma$$ instead of 2i$$\sigma$$

Last edited:
nrqed
Homework Helper
Gold Member

## Homework Statement

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

## The Attempt at a Solution

This is how I did..and I am getting
2$$i \sigma$$ 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?
Indeed, your first lines should be $\sigma_y\sigma_z-\sigma_z\sigma_y=2i\sigma_x$ etc.