On a General Theorem Relating to the Product of Two Determinants

[We have contributed in a series of papers our researches relating to the evaluation of certain classes of determinants to the Journal of the Indian Mathematical Society. The main results relating to persymmetrics have been communicated to the London Mathematical Society. In the course of our work, we have discovered a very elegant theorem, which has many interesting applications. In particular, we find that most of the results proved in our previous papers can be deduced from this theorem. This paper contains this theorem and some of its applications].