Matrix representation for (S1+S2)^2 operator

[martina]

Hi

I wasn't able to insert equations here, so here's the link where my problem is described:
http://www.advancedphysics.org/forum/showthread.php?t=7696

 

[martina]

I've derived the matrix using two different, but equivalent methods (the one described in the above link-Sakurai and by calculating the direct products of Pauli matrices) and it came out the same, yet its eigenvalues are not what I know they must be, so there must be something fundamentally wrong in my procedure, but I just can't detect it. If you happen to know how the matrix looks like without a detailed derivation, I'd be grateful for that too, cause I'm really stuck here