∴|a 1+a2; a2+a3; a3+a 1 | = | a 1+a2+a2+a3; a2+a3; a3+a 1|
= | a 1+a2+a2+a3+a3+a 1; a2+a3; a3+a 1|
= | 2(a 1+a2+a3); a2+a3; a3+a 1|
= 2 | a 1+a2+a3; a2+a3; A3+a 1|: The common factor of a series of determinants can be
Mentioned outside the determinant