Which matrices are idempotent (A2=AA^2 = AA2=A)?
(1001)\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}(1001)
(0000)\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}(0000)
(1100)\begin{pmatrix} 1 & 1 \\ 0 & 0 \end{pmatrix}(1010)
(2002)\begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}(2002)