Alexa claims that she can justify the divisibility test by 11. She says: I noticed that...

Alexa claims that she can justify the divisibility test by 11. She says: I noticed that each even power of 10 can be written as a multiple of 11 plus 1 and every odd power of 10 can be written as a multiple of 11 minus 1. In fact:

and so on.

Now I look at a four-digit number abed and proceed as in the divisibility by 3. I collect the parts that are divisible by 11 regardless of what the digits are and put together the rest, which is

d - c + b - a

Complete the details of Alexa's argument and justify the test for divisibility by 11.