Question

Let
A =$\begin{pmatrix} 4 & -2 \\\ \alpha & \beta \\\ \end{pmatrix}$
If A 2 + γ A + 18I = 0, then det (A) is equal to ______.

• A. –18
• B. 18
• C. –50
• D. 50

Answer 1

Answer: (B)

18

Answer 2

The correct answer is (B) : 18
Characteristic equation of A is given by
$|A-λI| = 0$
$\begin{vmatrix} 4 - \lambda & -2 \\\ \alpha & \beta - \lambda \\\ \end{vmatrix} = 0$
$⇒ λ^2-(4+β)λ + (4β + 2α) = 0$
So, $A^2 - (4+β)A + (4β+2α)I= 0$
$|A| = 4β+2α = 18$