Let $|w_2 \rangle = | + \rangle |-\rangle$ and $|w_3\rangle = |-\rangle |+\rangle$. Show that $\langle w_3 | w_3 w_2 \rangle = 0$.
I get $\langle w_3 | w_3 w_2 \rangle = (\langle - | \langle + | ) (| - \rangle |+\rangle |+\rangle |-\rangle$) but I'm not sure how to combine this into inner products.