Simple matrix equation I believe I'm missing an important concept and I need your help.
I have the following question:
"If $A^2 - A = 0$ then $A = 0$ or $A = I$"
I know that the answer is FALSE (only because someone told me) but when I try to find out a concrete matrix which satisfies this equation (which isn't $0$ or $I$) I fail.
Can you please give me a direction to find a concrete matrix? What is the idea behind this question?
Guy

If for a polynomial $p$ and a matrix $A$ you have $p(A)=0$ then for every invertible matrix $W$ you have $$p(W^{-1}AW)=W^{-1}p(A)W=0 . $$
Here $p=x^2-x$, you can take $A=\begin{pmatrix}1&0\\0&0\end{pmatrix}$, $W$ any invertible matrix to make a lot of examples.
