The statement is:
Show that if a matrix, A, is idempotent, then 2A-I is invertible and it is its own inverse.
I did
(2A-I)*I
=(2A-I)*A*A^-1
=(2A^2-A)*A^-1
=(2A-A)*A^-1
=A*A^-1 = I
and I is invertible, thus 2A-I is invertible.
Have I done something that is not always true here? or is 2A-I really equal to I? meaning A = I
(Idempotent means that A^n = A for any matrix A and n being an element of Z+
Just seems too neat