self-adjoint operators for Pauli-Runge vector

for the Pauli-Runge vector:

where denotes the Pauli-Runge operators, show that , and are self-adjoint operators

im a little confused as to what self-adjoint means. i have read that if then A is self-adjoint, but im not sure how to show that for this particular vector A! also, does it have anything to do with the commutation relations ?

also, do I have to show it for each of and or can I just show it for ?

i then have to show that where denotes the orbital angular momentum operators...im not sure how to do this either!!!