Suppose I have two matrices $A$ and $B$ and they satisfy the property that:
$A$ has non-zero values on row $j$ $\implies$ Row $j$ of $B$ contains only zero values.
$B$ has non-zero values on row $j$ $\implies$ Row $j$ of $A$ contains only zero values.
Is there a word for this relationship? Like, can I say they are some sort of "Orthogonal"?
I'm not aware of any such name either. But if you want a word to define and then use for a paper/problem you are writing up (i.e. a nonce word), I'd recommend describing them as complementary, rather than orthogonal.