In order to figure out if a given pure 2-qubit state is entangled or separable, I am trying to compute: the density matrix, then the reduced density matrix by tracing out with respect to one of the qubits, squaring the resulting reduced matrix, and finally taking its trace. Then, if the trace is $=1,$ I know the state is separable and entangled otherwise. So I am trying this method for the following state (which we know to be entangled): $$ |\psi\rangle = a_0b_0 |00\rangle+a_0b_1|01\rangle + a_1