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
but how is this A?
Thank you in advance!
Right off hand, the zero and identity matrices will have this property. That's at least two. What do they have in common? You probably aren't ready to understand the answer, but keep the question in mind until you are.
That will give you four simultaneous equations, not linear. Try solving them. You should wind up with eight possibilities, work through them.