Periodic matrices in SL(3,Z) will be conjugated to product of periodic matrices in SL(2,Z) by +- indentity on a third integer direction. Is this true?

Sorry, following your comments, maybe something I said is misleading. I state the original question: Consider a periodic automorphism $\phi$ on $Z^3$, can we find a coordinate on $Z^3$, such that $\phi$ is (1,0;0,A) or (-1,0;0,A).