Question

If the value of a third order determinant is $11$, then the value of the square of the determinant formed by the cofactors will be

• A. 11
• B. 121
• C. 1331
• D. 14641

Answer 1

Answer: (D)

${\Delta }^{\prime }={\Delta }^{n-1}$
$\therefore {\Delta }^{\prime }={\Delta }^{3-1}={\Delta }^2(\because n=3)$
$\Rightarrow {\Delta }^{\prime }={\Delta }^2$
$\therefore {\Delta }^{\prime }=(11{)}^2$
$\Rightarrow {\left({\Delta }^{\prime }\right)}^2={\left(11^2\right)}^2$
$=(11{)}^4=14641$