Question

If $A=\left[\begin{array}{cc}2& 4\\ k& -2\end{array}\right]$ and $A^2=O$, then find the value of k.

Answer 1

$A=\left[\begin{array}{cc}2& 4\\ k& -2\end{array}\right]$

$A^2=\left[\begin{array}{cc}2& 4\\ k& -2\end{array}\right]\left[\begin{array}{cc}2& 4\\ k& -2\end{array}\right]$

$=\left[\begin{array}{cc}4+4k& 8-8\\ 2k-2k& 4k+4\end{array}\right]=0$

$4k+4=0$

$k=-1$