I would like to know if these problems are NP-complete :
1) for two real matrices $A$ and $B$ there exists $P$ and $Q$ permutation matrices, such that $PAQ=B$
2)same question with $A$ and $B$ matrices whose entries are $0$ or $1$
3)same question if $A$ and $B$ are order matrices. What I call order matrix, is an $n\times n$ matrix $A$ whose entries are $0$ or $1$, such that there exists an ordered set $(\left\{a_1,a_2...a_n\right\},\leq_A)$ such that $A_{i,j}=1$ iff $a_i\leq_A a_j$.
where $A_{i,j}$ is the coefficient of $A$ that is both on $i$-th row and $j$-th column.
(2) effectively asks to find whether two bipartite graphs are isomorphic. This is equally difficult as recognizing graph isomorphism in general, which is widely suspected to be NP-intermediate.
(1) is the same, but for edge-labeled graphs. It can be reduced to (2) with a quadratic blowup in the size of the problem.
(3) appears to be trivial, unless I'm misunderstanding something: Any two "order matrices" of the same size are permutatively equivalent. (Or is $\le_A$ supposed to be a partial order?)