  Let $\mathbb{P}_n$ be the set of all matrices which have the same zero
patterns with some permutation matrix of order $n$.
  In this paper, we prove the following result: Let $\mathbb{I}$ be the unit
tensor of order $m\ge3$ and dimension $n\ge2$. Suppose that $P$ and $Q$ are two
matrices with $P\mathbb{I}Q=\mathbb{I}$, then $P,Q\in \mathbb{P}_n$. This gives
a characterization for the similarities of tensors with order $m\ge3$.
