I need to determine whether the following is (i)whether $X$ is a functor;
(ii)whether it is an affine scheme;
(iii) an $R$-algebra $A$ representing $X$ and a universal element of $X(A)$.
(a) $X(C) = \{x ∈C | x^2 = 1\lor x^3 = 1\}$
(b) $X(C) = \{M ∈Mat_{2×2}(C) | M^{100} = I\}$
I think may be (a) is not an affine scheme because so far I cannot find a universal element for it... Any ideas about that?
Also I think the second one is an affine scheme. But I am not able to find its presentation because lack of computation... How to express $M^{100}=I$ in polynomials?