Neutrino mass matrices with vanishing determinant

We investigate the prospects for neutrinoless double beta decay, texture zeros. and equalities between neutrino mass matrix elements in scenarios with vanishing determinant mass matrices for vanishing and finite θ₁₃ mixing angles in normal and inverse mass hierarchies. For normal hierarchy and both zero and finite θ₁₃ it is found that neutrinoless double beta decay cannot be observed by any of the present or next generation experiments, while for inverse hierarchy it is, on the contrary, accessible to experiments. Regarding texture zeros and equalities between mass matrix elements, we find that in both normal and inverse hierarchies with θ₁₃=0 no texture zeros nor any such equalities can exist apart from the obvious ones. For θ₁₃≠0 some texture zeros become possible. In normal hierarchy two texture zeros occur if 8.1×10^-2≤|sinθ₁₃|≤9.1×10^-2 while in inverse hierarchy three are possible, one with |sinθ₁₃|≥7×10^-3 and two others with |sinθ₁₃|≥0.18. All equalities between mass matrix elements are impossible with θ₁₃≠0.