Ohhhhhhh wow, that's a really good question. I was trying to solve it by looking at which nucleotide was changing, whether we were going from purine->pyrimidine, whether we formed a stop codon or a frame shift, etc. I didn't even consider the Southern blot aspect...
Basically when you do a Southern Blot, you add restriction enzymes (also called endonucleases) to the DNA you're interested in. These cut it up into chunks at certain points, called restriction sites. Then, you put the chunks in a gel, apply an electric field, and see how far the chunks of DNA migrate. Smaller chunks will migrate farther down the gel.
Restriction sites are palindromic. The point mutation in A screws up the palindrome, which will prevent the restriction enzymes from binding. This will mean DNA fragments from sample A will be different sizes than the fragments in the other samples, and we'll be able to identify them that way. Here is a decent picture: