no it wont
=MIN(IF(A:A=A2,B:B,""))
us control+shift+enter to enter as an array formula
it will then look like
{=MIN(IF(A:A=A2,B:B,""))}
with curly brackets
probably not a good idea to reference complete cells
so set the range
=MIN(IF($A2:$A$100000=A2,B$2:B$100000,""))