Question

-8 and 5 are the eigen value of a non-singular matrix A, then the eigen values of adj A are

• A. 16, -10
• B. -5, 8
• C. 5, -8
• D. -16, 10

Answer 1

The correct option is C 5, -8

$A^{-1}=\frac{\left(adjA\right)}{|A|}$

$|A|=-8\times 5=-40$

$|A|\left(A^{-1}\right)=\left(adjA\right)$

$\lambda ofadjA=\frac{|A|}{{\lambda }_1},\frac{|A|}{{\lambda }_2}=\frac{-40}{-8},\frac{-40}{5}$

$\lambda =5,-8$