Question

Find a nonzero matrix A for which A^2=0.

Answer 1

@Hero, @thomaster

Answer 2

try \[\left[\begin{matrix}1-i~~&1+i\\1+i~~&1-i\end{matrix}\right]\]

Answer 3

@zepdrix can you help her a real entries matrix?

Answer 4

for real entries matrix, you have a lot of them.
just take (A-\(\lambda I)^2\) you have 0 matrix.
for example: \(A = \left[\begin{matrix}0&-2\\2&4\end{matrix}\right]\) so, eigenvalue is 2 double roots. Then \(A-\lambda I= \left[\begin{matrix}-2&-2\\2&2\end{matrix}\right]\) . This matrix square = 0 matrix. ALWAYS.
From this, you can construct any matrix whose square =0