(1) Show that the sum of two Hermitian operators a and b is also a Hermitian operator.
(2) Show that the product of a Hermitian operator with itself is also a Hermitian operator.

a) The sum of Hermitian operators is Hermitian; the product may not be.
b) The sum of Hermitian operators may not be Hermitian; the product is.
c) Both the sum and product of Hermitian operators are always Hermitian.
d) Neither the sum nor the product of Hermitian operators is necessarily Hermitian.