An operator is said to be linear if it obeys the distributive law and commutes with the constant i.e.
$\hat{A}(a_1 |\psi_1\rangle + a_2|\psi_2\rangle)=a_1\hat{A}|\psi_1\rangle +a_2\hat{A}|\psi_2\rangle$ and same when we act in from bra. The product of two operator are not commutative (not all case) but their product are associative.
So in evaluating $\langle\phi|\hat{A}|\psi\rangle$, it does not matter if one first applies $\hat{A}$ to the ket and then takes the bra-ket or one first applies $\hat{A}$ to the bra and then takes the bra-ket i.e.
$(\langle\phi|\hat{A})|\psi\rangle=\langle\phi|(\hat{A}|\psi\rangle)$.
My question is does this associative property holds for linear operator too as in many text i have read they never talked about how anti-linear operator commutes as such and does it matter as stated above for linear operators that the order dosent matter as such.
Edit:- I know the property of anti-linear operator that it makes the constant complex when an operator applies on it. Would love answer's if the discussion is based on the notation of bra and ket as i am comfortable on this notation.