gcc has a -frecord-gcc-switches
option for that:
-frecord-gcc-switches
This switch causes the command line that was used to invoke the compiler to
be recorded into the object file that is being created. This switch is only
implemented on some targets and the exact format of the recording is target
and binary file format dependent, but it usually takes the form of a section
containing ASCII text.
Afterwards, the ELF executables will contain .GCC.command.line
section with that information.
$ gcc -O2 -frecord-gcc-switches a.c
$ readelf -p .GCC.command.line a.out
String dump of section '.GCC.command.line':
[ 0] a.c
[ 4] -mtune=generic
[ 13] -march=x86-64
[ 21] -O2
[ 25] -frecord-gcc-switches
Of course, it won’t work for executables compiled without that option.
For the simple case of optimizations, you could try using a debugger if the file was compiled with debug info. If you step through it a little, you may notice that some variables were ‘optimized out’. That suggests that optimization took place.