can you please show all steps steps

(1) For example, think about the elementary Pauli Spin Matrices P = 0 1 10 ,9= 0 7 ).R-C. Check (but don't show) that PP = OO = RR = /; also that each of P. O, R has eigenvalues 1. -1. Check (again you don't have to show me) that PO=iR. OR iP. RP=10. (a) Let a, b, c be real numbers (not all zero) and define the general Pauli Spin Matrix S = aP+bQ+cR. What are trace(A), der(A)? trace( S ) = det( S) = Express the eigenvalues of S in terms of a, b, c. Check (don't show) that the sum of the eigenvalues = trace(A) and the product of the eigenvalues = der(A)