We consider Matsumoto change of Finsler metrics. First, we find a condition under which the Matsumoto change of a Finsler metric is projectively related to it. Then, considering the subspace of $m$-th root Finsler metrics, if $\bar F$ is the Matsumoto change of $F$, we prove that $\bar F$ is locally projectively flat if and only if it is locally dually flat. In this case, $F$ and $\bar F$ reduce to locally Minkowskian metrics.