Answer
There is the zero matrix $O$ which satisfies that $O^{2}=O$
(Other answers are possible.)
Work Step by Step
One singular matrix which is of order 2 is the zero matrix
$O_{2\times2}=\left[\begin {array}{cc}
0&0\\
0&0
\end {array}\right]$
The zero matrix satisfies $O^{2}=O$
