Question

If A=$\left|\begin{array}{cc}2& 4\\ k& -2\end{array}\right|$ and $A^2=0$ then find the value of k

• A. -4
• B. -3
• C. -2
• D. -1

Answer 1

The correct option is D -1

$A^2=0$
$=>\left|\begin{array}{cc}2& 4\\ k& -2\end{array}\right|\times \left|\begin{array}{cc}2& 4\\ k& -2\end{array}\right|=\left|\begin{array}{cc}0& 0\\ 0& 0\end{array}\right|$
$\left|\begin{array}{cc}2\left(2\right)+4\left(k\right)& 2\left(4\right)+4(-2)\\ k\left(2\right)+(-2)\left(k\right)& k\left(4\right)+(-2)(-2)\end{array}\right|=\left|\begin{array}{cc}0& 0\\ 0& 0\end{array}\right|$
$\left|\begin{array}{cc}4k+4& 0\\ 0& 4k+4\end{array}\right|=\left|\begin{array}{cc}0& 0\\ 0& 0\end{array}\right|$
$=>4k+4=0$
$=>k=-1$