https://tex.z-dn.net/?f=An%5C+idempotent%5C+matrix%5C+is%5C+a%5C+matrix%5C+n%5Ctimes+n%5C+%28square%5C+matrix%5C+A%29%5C+which%3AA%5E2%3DA%5C%5C%5C%5CExample%3A%5C%5C++A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-1%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D%5C%5CA%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-1%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-1%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5Ccdot2-1%5Ccdot2%262%5Ccdot%28-1%29-1%5Ccdot%28-1%29%5C%5C2%5Ccdot2-1%5Ccdot2%262%5Ccdot%28-1%29-1%5Ccdot%28-1%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4-2%26-2%2B1%5C%5C4-2%26-2%2B1%5Cend%7Barray%7D%5Cright%5D+%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-1%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D+%3DA