Sorry for this second question!

How do I prove that A^2 = A in Matrices given that AB=A and BA=A.

I tried to expand the LHS and then intend to get at AB so as to end up with RHS=A in the end but I'm stuckm

A^2 = A

AA = A

A(AB) = A

...

If I keep expandin, I'll keep getting more Bs and As..

Please help me.

Thank you!