A matrix [tex]a[/tex] is idempotent if [tex]a^2=a[/tex]. Find a basis for the vector space of all 2x2 matrices consisting entirely of idempotents
2. The attempt at a solution
the vector space in question is dimension 4, so I need to find 4 idempotent matrices.
but i don't want to find them by 'guessing'. Is there a good way to find them?