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? 

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Sorry, following your comments, maybe something I said is misleading. I state the original question:
   Consider a periodic homeomorphism $f$ on $T^3$, can we always find a coordinate on $T^3$, such that $f$ is either $\left(
                              \begin{array}{cc}
                                1 & 0 \\
                                0 & A \\
                              \end{array}
                            \right)$
                            
                            or
                            
                            $\left(
                              \begin{array}{cc}
                                -1 & 0 \\
                                0 & A \\
                              \end{array}
                            \right)$.