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\langle+|\rho|+\rangle = \begin{bmatrix}1/\sqrt{2} & 1/\sqrt{2}\end{bmatrix}\begin{bmatrix}1/2 & 0 \\ 0 & 1/2\end{bmatrix}\begin{bmatrix}1/\sqrt{2} \\ 1/\sqrt{2}\end{bmatrix} = \dfrac{1}{2}.