In the present paper, I have re-examined the weak basis invariants at low energies, proposed by C. Jarlskog and Branco et. al, respectively, in their earlier analyses, after confronting them with the assumptions of two zeros and an equality between arbitrary non-zero elements in the Majorana neutrino mass matrix in the flavoured basis. This particular conjecture is found to be experimentally feasible as shown by S. Dev and D. Raj in their recent work. The present analysis attempts to find the

more »

... cessary and sufficient condition for CP invariance for each experimentally viable ansätz, pertaining to the model along with some important implications.