Exercise 3.8 Discussion

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 3.8}$

a) Show that $\frac{1}{\sqrt{2}}(\ket{0}\ket{0} + \ket{1}\ket{1})$ and $\frac{1}{\sqrt{2}}(\ket{+}\ket{+} + \ket{-}\ket{-})$ refer to the same quantum state.
b) Show that $\frac{1}{\sqrt{2}}(\ket{0}\ket{0} - \ket{1}\ket{1})$ refers to the same state as $\frac{1}{\sqrt{2}}(\ket{\i}\ket{\i} + \ket{-\i}\ket{-\i})$.