APL (Dyalog Unicode), 1012 bytes
Anonymous tacit prefix function.
⊂(∨/¨⍳∊¨1=,¨⊂1∊⊢)¨⍳ ⊂(…)¨⍳ apply the following tacit infix function between the entire argument and each index in an array of those dimensions:
1∊⊢ is there a 1 in the index?
=, prepend a Boolean list indicating which coordinate are equal to the corresponding element of the original argument
∨/ are any true? (lit. OR reduction)