In quantum mechanics, the action of a projection operator $\hat{P}$ acting on a quantum mechanical system, prepared in a state $| \psi \rangle$, is described by the eigenvector equation
$\hat{P} | \psi \rangle = c | \psi \rangle $ where $c \in \mathbb{C}$.
How can I show that $trace(|\psi\rangle \langle \psi | \hat{P}) = \langle \psi | \hat{P} | \psi \rangle $?