\documentclass[a4paper,12pt]{article}

\begin{document}

\parindent=0pt


QUESTION Find a $2\times 2$ matrix $A$ with no zero entries but
with $A^2=0$.

\bigskip


ANSWER

Any matrix of the form $$A=\left[\begin{array}{cc}a&b\\
-\frac{a^2}{b}&-a\end{array} \right]$$ satisfies $A^2=0$.


\end{document}