Question

If $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ (where bc $\ne$ 0) satisfies the equations $x^2+k=0$, then

• A. $a+d=0$
• B. $k=-|A|$
• C. $k=|A|$
• D. none of these

Answer 1

Answer: (C)

$k=|A|$

since $mat\left(A\right)$ contains no terms of x hence determinant of $mat\left(A\right)$ is constant quantity.

Hence $k=|A|$

As k and x both are constant quantities