Find all symmetric 2x2 matrices A such that A^2 = 0.
thank you very much.
Where are you stuck with this problem?
There may be a more elegant solution, but I personally would just solve,
$\displaystyle \left( \begin{array}{cc}
a & b \\
c & d \\
\end{array} \right)\left( \begin{array}{cc}
e & f \\
g & h \\
\end{array} \right)=
\left( \begin{array}{cc}
0 & 0 \\
0 & 0 \\
\end{array} \right)
$
whilst remembering that either ad=bc or eh=gf (where did I get these from?).
You get 4 equations in 8 unknowns, but this doesn't actually matter because all it means is that your solutions won't be unique.
(That is, there is more than one possible solution to your equations. For example, a=b=c=d=0, all the others whatever, and a=b=c=0, d=1=e,, f=g=h=0 are two different solutions.)