Answer
a. Yes, it can be shown. They are equal only when the spin is zero.
b. No.
Work Step by Step
a. From equation 41.22, we see that the magnitude of the orbital angular momentum is $\sqrt{l(l+1)}\hbar$.
From equation 41.23, we see that the component of the orbital angular momentum along any direction is at most $m_l \hbar$, where the maximum value of $m_l$ is $l$. Therefore the first quantity is always greater than or equal to the second.
They are equal only in the case when $l=0$.
b. This is not true for a classical object, where the component of the angular momentum vector may be equal to the magnitude of the vector itself.
