Ex10 10

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.10}$

For $\ket\psi \in A\otimes B$, show that $\ket\psi$ is unentangled if and only if $S(\tr_B\rho) = 0$, where $\rho = \ket\psi\bra\psi$.