(a) Check that the spin matrices (Equations 4.145 and 4.147) obey the fundamental commut...

(a) Check that the spin matrices (Equations 4.145 and 4.147) obey the fundamental commutation relations for angular momentum, Equation 4.134.

(b) Show that the pauli spin matrices (Equation 4.148) satisfy the product rule

Where the indices stand for x, y, or z and is the Levi-Civita symbol: +1 if jkl = 123, 231, or 312; -1 if jkl = 132, 213, or 321; 0 otherwise.