Creating new rows by combining existing rows excel

I am fairly new here, so if this go against the rules please tell me.

I have an issue that seems pretty simple but I wanted to check to make sure. I have been trying to see if I could create a new row by combining every variable from one column with another, like so:

 Column 1       Column 2        Combined 
    A               1              A1
    B               2              A2
                    3              A3
                                   B1
                                   B2
                                   B3

But instead of typing the combinations manually, I wanted the combined column make this combination without user input and to update automatically whenever column 1 or 2 has a row added or removed. I have been trying to figure out if there is some way to use the concatenate function in excel or the & sign but neither methods seems to work. I was thinking trying to code this in visual basics.

The main question: is this possible to do in excel? If so which function(s) could I use?