A matrix $A$ is called idempotent if $A^2=A.$
If $$A=α\begin{pmatrix}-\frac{3}{2}&1\\ -3&2\end{pmatrix}$$ is idempotent, find α.
How can I solve this question? Do I just need to insert α into the matrix and equal to zero? I need help regarding this question. I try to solve it for hours but I cannot understand it
$A=a\begin{pmatrix}-1.5& 1\\ -3 &2\end{pmatrix}$. $A^2=a^2\begin{pmatrix}-0.75& 0.5\\ -1.5 &1\end{pmatrix}$
As $A^2=A$, $2a=a^2\implies a(2-a)=0\implies a=0$ or $a=2$.
I am not sure where you had problem (as it is straight-forward), so I am writing the answer explicitly.