V = Mnxn is a space vector formed by all the square matrices.
Is W = {A in Mnxn : A^x = A} a subspace of V?
Thanks
No, because if A is in W, then
B = lambda A
is not in W if lambda is not equal to 1:
A^x = A --->
B^x = lambda^x A^x = lambda^x A =
labda^(x-1) B
which is not equal to B for general lambda.