Question

Let ${\Delta }_0=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]$ (where ${\Delta }_0\ne 0$) and let ${\Delta }_1$ denote the determinant formed by the cofactors of elements of ${\Delta }_0$ and ${\Delta }_2$ denote the determinant formed by the cofactor at ${\Delta }_1$ and so on ${\Delta }_n$ denotes the determinant formed by the cofactors at ${\Delta }_{n-1}$ then the determinant value of ${\Delta }_n$ is

• A. ${\Delta }_0^{2n}$
• B. ${\Delta }_0^{2^n}$
• C. ${\Delta }_0^{n^2}$
• D. ${\Delta }_0^2$

Answer 1

The correct option is B ${\Delta }_0^{2^n}$

${\Delta }_1={\Delta }_0^2,{\Delta }_2={\Delta }_1^2={\Delta }_0^{2^2}$
$\therefore {\Delta }_n={\Delta }_0^{2n}$