Arthur Cayley

“ If, to get rid of this arbitrary common factor, we assume that the product of the elements in the dexter diagonal has the coefficient +1, we have a complete definition of the determinant, and it is interesting to show how from these properties, assumed for the definition of the determinant, it at once appears that the determinant is a function serving for the solution of a system of linear equations. ”

“ Any determinant
formed out of the elements of the original determinant, by selecting the lines and columns at pleasure, is termed a minor of the original determinant; and when the number of lines and columns, or order of the determinant, is n−1, then such determinant is called a first minor; the number of the first minors is=n 2, the first minors, in fact, corresponding to the several elements of the determinant—that is, the coefficient therein of any term whatever is the corresponding first minor. ”

“ The first minors, each divided by the determinant itself, form a system of elements inverse to the elements of the determinant.
A determinant is symmetrical when every two elements symmetrically situated in regard to the dexter diagonal are equal to each other ”