Question

Calcule todas as matrizes X, quadradas de ordem 2, tais que X² = X

Answer 1

$X^2=X\\\\X^2-X=0\\\\X(X-I)=0\\\\(X-0)(X-I)=0\left\langle\begin{matrix}X-0=0\longrightarrow{X}=0\\\\X-I=0\longrightarrow{X}=I\end{matrix}\right\\\\\\\boxed{S=\left\{\left[\begin{array}{aa}0&0\\0&0\end{array}\right];\ \left[\begin{array}{aa}1&0\\0&1\end{array}\right]\right\}}$


$\mathrm{S\tilde{a}o\ as\ matrizes\ nula\ e\ identidade.}$