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## Homework Statement

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?

Thanks