Take \b[$A=\begin{pmatrix}0&1\\1&0\end{pmatrix}$]. It has exactly two nonzero entries, both one, but $A^2=I_2\ne A$. Thus it is not an <idempotent matrix>. Its being an <orthogonal matrix> does not make it an <orthogonal projector>.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof / 5 / d / Solution

 Solution (source code)