Please help me solving these problems. Thanks in advance.
a) find the degree of a minimal splitting field of (x^6 + 1) over Q.
b) if a is a any algebraic number prove that there exists a positive integer 'n' such that 'na' is an algebraic number.
c) if W is a subspace of V and vєV satisfies (v,w) + (w,v) = (w,w) for all wєW prove that (v, w)=0 for all wєW where V is inner product space over F.
d) if T1,T2 є Hom(V,W), then show that
1) r(α(T1))=r(T1) for all αєF, α≠0
2) | r(T1)-r(T2) | ≤ r(T1+T2) ≤ r(T1) +r(T2), where r(T) means rank of T.