The x86 tag wiki contains a list of resources that you can use to look up information on various instructions. For example, searching for IMUL on http://www.felixcloutier.com/x86/ leads you to http://www.felixcloutier.com/x86/IMUL.html.
So it depends, how your assembler will compile it, if two operand variant is used, then result is truncated, if single operand (IMUL ebx) is used, then result is in edx:eax.
About flags: probably debug to be sure, but the two operand version, if I'm reading it correctly will set CF/OF when the result is truncated, so in your case CF=1, OF=0? (unsigned trunc, signed not overflow).
After 3h later...
It occurred to me, that I actually should search again for some nice linux debugger, like "TD" from Borland in DOS era, because it may have be handy to have one.
There's of course the gdb always around, but I can't get to like it (especially as it usually goes with AT&T syntax, which I personally dislike).
So I tried "ddd" (Data Display Debugger), directly available in Ubuntu repositories, but it looks a bit old (yeah, MOTIF, if you know, what I mean, if you never heard MOTIF, then you are not old enough). And it's gdb based... Probably worth of mention here, for people who want to go in GNU path, but I searched further.
And I ended up downloading and compiled edb-debugger. After few tries I got it to compile on my older ubuntu, run it .. and... that's IT. Just few clicks in preferences, and "TD" feel is here.
So, I tried your instructions (had to compile first some helloworld.asm from NASM examples to have some test linux binary to run, then you can directly overwrite instructions in debugger for these short questions).
After IMUL eax,ebx the changes to CPU state are:
eax = 0xe0000001
CF = 1, OF = 1, SF = 1, ZF = 0, PF = 0, AF = 0, ...
After IMUL ebx the changes to CPU state are:
eax = 0xe0000001
edx = 0x00ffffff
CF = 1, OF = 1, SF = 1, ZF = 0, PF = 0, AF = 0, ...
(so in this case flags are the same).
I strongly suggest to you to get some nice debugger too, to stop asking questions like these. If it wouldn't be along my own interest to get one debugger running, I wouldn't bother to answer.