If the co factors of the elements a1,b1,c1 .... are A1,B1,C1,...are respectively then the value of the determinant Δ=a1    b1    c1a2    b2    c2a3    b3    c3, Δ≠0, then the value of B2    C2B3    C3 is equal to

B2=a1c3−a3c1,C2=−a1b3−a3b1B3=−a1c2−a2c1,C3=a1b2−a2b1∴ B2C2B3C3=a1c3−a3c1−a1b3+a3b1−a1c2+a2c1a1b2−a2b1=a1c3−a1b3−a1c2a1b2+a1c3a3b1−a1c2−a2b1+−a3c1−a1b3a2c1a1b2+−a3c1a3b1a2c1−a2b1                         =a12c3−b3−c2b2+a1b1c3a3−c2−a2+a1c1−a3−b3a2b2+b1c1−a3a3a2−a2                         =a1a1b2c3−b3c2−b1a2c3−a3c2+c1a2b3−a3b2                        =a1a1    b1    c1a2    b2    c2a3    b3    c3=a1Δ