Let a and b alpha belongs to c then the absolute value of the sum of all value of alpha for which detab=0

Question

Let \( A =\left[\begin{array}{rrr}1 & -2 & \alpha \\ \alpha & 2 & -1\end{array}\right] \) and \( B =\left[\begin{array}{rr}2 & \alpha \\ -1 & 2 \\ 4 & -5\end{array}\right], \alpha \in C\). Then the absolute value of the sum of all values of \( \alpha\) for which \(( \operatorname{det}(A B)=0\) is : 

(A) 3 

(B) 4 

(C) 2 

(D) 5

Answer 1

Correct option: (A) 3

Given,

Given,

\(\therefore\) Sum of all values of \(\alpha=-1-2=-3\)

\(\therefore\) Absolute value of  \(\alpha=|-3|=3\)