Texture one zero Dirac neutrino mass matrix with vanishing determinant or trace condition

In the light of non-zero and relatively large value of rector mixing angle (${\theta }_{13}$), we have performed a detailed analysis of texture one zero neutrino mass matrix $M_{\nu }$ in the scenario of vanishing determinant/trace conditions, assuming the Dirac nature of neutrinos. In both the scenarios, normal mass ordering is ruled out for all the six possibilities of $M_{\nu }$, however for inverted mass ordering, only two are found to be viable with the current neutrino oscillation data at 3σ confidence level. Numerical and some approximate analytical results are presented.