- elf-arch <file>
says the arch of given binary
- elf-arch -a <arch> <file>
checks if <file> matches ABI <arch>
elf-arch detects the kernel ABI needed to run a given binary, and prints its Debian arch name. This doesn't necessarily mean the arch can actually run that program/library: markings available in the ELF header are pretty much restricted to just word width, endianness and instruction set family. Architectures can also differ by the set of syscalls they use (although these can usually be mixed) or required CPU instructions; you can't generally distinguish between those other than trying to run the program.
The difference usually shows in the kernel refusing to run a binary vs executing it and crashing at runtime.
Thus, as far as ELF markings are concerned, there's often a set of Debian architectures which are aliases for the same kernel arch.
With this option, elf-arch instead of printing the detected architecture will check if <arch> matches one of aliases for the file, and return an exit code: 0 if there's a plausible match, non-zero if the given arch won't even try executing that file.