An\ idempotent\ matrix\ is\ a\ matrix\ n\times n\ (square\ matrix\ A)\ which:A^2=A\\\\Example:\\  A=\left[\begin{array}{ccc}2&amp;-1\\2&amp;-1\end{array}\right]\\A^2=\left[\begin{array}{ccc}2&amp;-1\\2&amp;-1\end{array}\right]\cdot\left[\begin{array}{ccc}2&amp;-1\\2&amp;-1\end{array}\right]=\left[\begin{array}{ccc}2\cdot2-1\cdot2&amp;2\cdot(-1)-1\cdot(-1)\\2\cdot2-1\cdot2&amp;2\cdot(-1)-1\cdot(-1)\end{array}\right]\\=  \left[\begin{array}{ccc}4-2&amp;-2+1\\4-2&amp;-2+1\end{array}\right] =  \left[\begin{array}{ccc}2&amp;-1\\2&amp;-1\end{array}\right] =A