if `A_(1) ,B_(1),C_(1) …….` are respectively the cofactors of the elements `a_(1) ,b_(1),c_(1)……` of the determinant
`Delta = |{:(a_(1),,b_(1),,c_(1)),(a_(2),,b_(2),,c_(2)),(a_(3),,b_(3),,c_(3)):}|, Delta ne 0 ` then the value of `|{:(B_(2),,C_(2)),(B_(3),,C_(3)):}|` is equal to

Let A= |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3)c_(3))| then the cofactor of a_(31) is:

Prove that the value of each the following determinants zero: (a)|{:(a_(1),,la_(1)+mb_(1),,b_(1)),(a_(2),,la_(2)+mb_(2),,b_(2)),( a_(3),,la_(3)+mb_(3),,b_(3)):}|

If A_(i),B_(i),C_(i) are the cofactors of a_(i),b_(i),c_(i) respectively,i=1,2,3 in Delta =|(a_(1),b_(2),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| show that |(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))|=Delta^(0)

(a) If A=((4,2),(-1,x)) and such that (A-2I)(A-3I)=0. find the value of x. (b) If A_(i),B_i,C_(i) are the cofactors of a_(i),b_(i),c_(i) , respectively, i=1 to 3 in |A|=|(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(3)),(a_(3),b_(3),c_(3))| , show that |(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))|=|A|^(2) .

which of the following is // are true for Delta= |{:(a^(2),,1,,a+c),(0,,b^(2)+1,,b+c),(0,,b+c,,c^(2)+1):}| ?

Prove that Delta = |{:(1,,1,,1),(a,,b,,c),(bc+1^(2),,ac+b^(2),,ab+c^(2)):}| = 2(a-b)(b-c)(c-1)

If A+iB=(a_(1)+ib_(1))(a_(2)+ib_(2))(a_(3)+ib_(3)) then A^(2)+B^(2) is :

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|