1.) Given A and B are both hermitian operators,

a.) Prove the product $\displaystyle AB$ will be hermitian only if $\displaystyle A$ and $\displaystyle B$ commute

b.) Prove $\displaystyle (A+B)^n$ is hermitian.

2.) Through the use of dirac notation, prove the eigenstates of a hermitian operator that belong to 2 different eigenvalues are orthogonal