VB Code to apply a formula to entire column

Hi All

I try to explain what I need to do.(for some reason I can not attached a worksheet=, and I will appreciate if the code is given to me in the body of the email using #Code)

Col A Col B Col C
111 2222 False
222 2222 False
.
.
.
.
.
..
to end row

I need to write a VB code (and I know I can just use a formula to do this but I need this for another functions and other manipulations and hence need VB code)

I have two columns and want to see whether the two columns match, i.e. I need to apply the following formula in col c2 if(a2=b2,"Yes","No")
and I need to repeat the same formula for all the rows until I reach the end of the file. My actual sheet has 100 of thousands of rows and has other functions in there, but If I can gte this code then I can perform other operations which I need.

Any help is appreciate it

Sub T()

Range("C2").FormulaR1C1 = "=if(RC[-1]=RC[-2],""Yes"",""NO"")"
Range("C2:c" & Cells(Rows.Count, 1).End(xlUp).Row).FillDown
End Sub

Thank you so much, this worked perfectly