Didn't know where to put this question, but apologies if I had picked the wrong place to put this in!

Find all 2x2 matrices A for which A^2 = A.

They gave me a hint which is to let A be $\displaystyle \begin{bmatrix} a & b \\c & d\end{bmatrix}$

$\displaystyle \begin{bmatrix} a & b \\c & d\end{bmatrix}$ $\displaystyle \begin{bmatrix} a & b \\c & d\end{bmatrix}$ gave me

$\displaystyle \begin{bmatrix} a^2+bc & ab+bd \\ac+cd & bc+d^2\end{bmatrix}$

but how is this A?

Thank you in advance!