let G=3^n, n is all integers. show that multiplication is an operation on G and show that is an abelian group

Let (G, ) be a group. Define a new binary operation * on G by the formula a * b = b · a for all a and bEG Show that the group (G, *) is isomorphic to the group (G, )

Show that any element of the Euclidean group is an isometry of R^n

Let d≥ 1 and let F be a field, and define a group of matrices G ≤ GLd+1(F) by A = {(^ ;) Prove that G is isomorphic to the group G A 1 € GL₁(F), v € Fª}. Affa(F) = {TA,v: A = GLd(F), v € Fd} considered in the previous question. (You do not need to prove that G is a group.)