Question

$A=\left[\begin{array}{cc}2& 4\\ -1& -2\end{array}\right]$ is a nilpotent matrix.

• A. True
• B. False

Answer 1

The correct option is A

True

$A=\left[\begin{array}{cc}2& 4\\ -1& -2\end{array}\right]$

Now $A^1\ne 0$

Check $A^2=\left[\begin{array}{cc}2& 4\\ -1& -2\end{array}\right]\left[\begin{array}{cc}2& 4\\ -1& -2\end{array}\right]$

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

Which is a null matrix. Hence A is a nilpotent matrix.