How to construct a matrix $A$ 
Construct a matrix $A$ such that $A^2\ne 0$ but $A^3=0$.

I need your help to find $A$. Please help. Thanks in advance.
 A: $$\text{Let} \;\;\;A = \begin{pmatrix} 0 & 2 & 0 \\ 0 & 0 & 2 \\ 0 & 0 & 0 \end{pmatrix}$$
$$\text{Then} \;\;\;\; A^2 = \begin{pmatrix} 0 & 0 & 4 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \neq \bf 0$$
$$\text{But} \;\;\;\; \;A^3 = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} = \bf 0$$
A: Regarding to @Julian's comment, take $A=\begin{pmatrix}
  0 & 1\\
  0&0
\end{pmatrix}$, Or $A=\begin{pmatrix}
  0 & 0 & 1\\
  0 & 0 & 0 \\
  0 &1 &0 
\end{pmatrix}$
A: Hint:
Generally, when you have a zero matrix with the line above the diagonal filled by zeros, you have that:
$$\left(\begin{matrix}
  0 & 1 & 0 & \dots &0&0 \\
  0 & 0 & 1 & \dots & 0&0\\
  \vdots & \vdots & \vdots & & \vdots & \vdots \\
  0&0&0&\dots&1&0\\
  0 & 0 &0 &\dots &0 & 1\\
 0&0&0&\dots&0&0
 \end{matrix}\right)^2=\left(\begin{matrix}
  0 & 0 & 1 &0&\dots &0&0 \\
  0 & 0 & 0  &1&\dots & 0&0\\
  \vdots&\vdots&\vdots&\vdots&&\vdots&\vdots\\
  0&0&0&0&\dots&0&1\\
  0&0&0&0&\dots&0&0\\
  0&0&0&0&\dots&0&0
 \end{matrix}\right)$$
Basically, the diagonal of ones moves up a line, if you make the do $A^3$, then the line of ones will move up another line (try it with a 3x3 matrix). So seeting it up properly, you can make it vanish to zero when you want.
