Let `Delta_(0)=|{:(a_(11),a_12,a_13),(a_(21),a_22,a_23),(a_(31),a_32,a_33):}|` and `Delta_(1)` denotes the determinant formed by the cofactors of elements of `Delta_(0)` and `Delta_(2)` denots the determinant formed by the cofactors of `Delta_(1)` and so on `Delta_(n)` denotes the determinant formed by the cofactors of `Delta_(n-1)` is

Options

A. `|A|^(2n)`
B. `|A|^(2n)`
C. `|A|^(n^(2))`
D. `|A|^(2)`

Answer

B

Explanation

Clearly,
`|A_(1)| = |A|^(2), |A_(2)| = |A_(1)|^(2),..., |A_(n)| = |A_(n-1)|^(2)`
`:. |A_(n)| = (|A_(n-2)|^(2))^(2) " " [ :' |A_(n-1)| = |A_(n-2)|^(2)]`
`rArr |A_(n)| = (|A_(n -2)|)^(2xx2)`
`rArr |A_(n)| = (|A_(n-3)|^(2))^(2xx2) = |A_(n-3)|^(2 xx 2 xx2)`
`rArr |A_(n)| = ...= |A|^(2 xx 2 xx 2 xx...xx 2n- " times") = |A|^(2n)`