I have read with much interest Professor Tait's “Note on Determinants of the Third Order” in the Proceedings of this Session (pp. 59–61), and admire the method of discovering new properties of Determinants. I am not sure, however, that the properties, when discovered, are more difficult of proof by Determinant methods, and I venture to submit the following as simple and elementary:—

The first property, namely,

is true under greater generality, and the Determinant proof is the same as for the special case.