Show operator is diag in second basis

[Old Guy]

Homework Statement

Show explicitly using Pauli matrices that the S² operator is diagonal in the second basis.

Homework Equations

S²=S$$^{2}_{1}$$+S$$^{2}_{2}$$+2S$$_{1}$$S$$_{2}$$

3. The Attempt at a Solution [/b]
In the last term, 1 and 2 are supposed to be subscripts, and the two S's should be shown as a dot product.

Treat as a 2-particle system; what are they looking for? What does "in the second basis" mean? There is also a chance that the probelm statement is incorrect; in the instructor's superscripts, it's often impossible to distinguish a 2 from a z. Thanks in advance.

 

[gabbagabbahey]

Is this really the entire problem?