So do I

To economise the use of words, there are certain ways you can use to achieve this aim. One of them is explained below.

You use 'So do I' in response to 'My brother likes to eat ice cream.' as uttered by my brother.

Look at some other examples below:
1 She did not come to school yesterday.
So did her sister.
[The longer sentence is Her sister did not come to school yesterday too.]

2 They play badminton in the evening daily.
So does she.
[The longer sentence is She plays badminton in the evening daily too.]

So much for economising the use of words.