Retains the same value, however the suffixes be **permuted**, we shall obtain a i 7 2 ar a2 a33?Q"l 7r2 rr3 w hich in r a l sum of terms, such as w!

It further appears that a determinant is a linear function' of the elements of each column thereof, and also a linear function of the elements of each line thereof; moreover, that the determinant retains the same value, only its sign being altered, when any two columns are interchanged, or when any two lines are interchanged; more generally, when the columns are **permuted** in any manner, or when the lines are **permuted** in any manner, the determinant retains its original value, with the sign + or - according as the new arrangement (considered as derived from the primitive arrangement) is positive or negative according to the foregoing rule of signs.