Question

If $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ (where $bc\ne 0{)}^{10}$ satisfies the equation $x^2+k=0$ then ?

• A. $a+d=0$
• B. $k=-|A|$
• C. $k=|A{|}^2$
• D. $Noneofthese$

Answer 1

The correct option is A $a+d=0$

$A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]A^2=\left[\begin{array}{cc}{a}^2+bc& ab+bd\\ ac+cd& bc+d^2\end{array}\right]A^2=\left[\begin{array}{cc}-K& 0\\ 0& -K\end{array}\right]\therefore a+d=0$