This question may sound weird, but it’s needed for injecting code to a binary.
Can you think of a way to make eax equal to 1, without depending on content like carry flag or others, other registers etc ?
But in 2 bytes only. 3 is easy and it can be done in many ways, but can it be done with 2 ?
I suspect you mean 2 bytes, not 2 opcodes. If you really mean 2 opcodes, then the following 3-byte alternatives come to mind:
I can’t immediately think of a two-byte sequence that would do the equivalent – I suspect there are none.