Discrete Mathematics

If $A \times B = B \times A$, (Where A and B are general matrices) then
(i) $A=I$
(ii) $A=B'$
(iii) $B=A$
(iv) $A'=B$

Which of the following pair is not congruent modulo 7?
(i) 10, 24
(ii) 25, 56
(iii) -31, -15
(iv) -64, -15

Let $\Psi : G \rightarrow H$ be a homomorphism of groups. Show that if $a \in G$ has order $n$, then $\Psi (a) \in H$ has order dividing $n$.