I have a definition of a property and I need to show that a structure has that property?
How can I do it? I know indeed that the structure has that property. I tried that property for some elements and It worked now I want to show that works for all.
that property means that each b in G occurs exactly once in each row, and each column of your table.
there is a unique x in G such that a*x = b means that in the row corresponding to "a", b only occurs in the "x" column.
there is a unique y in G such that y*a = b means that in the column corresponding to "a", b only occurs the "y" row.
for the table you have given, you may verify this by counting instances of each element of {1,2,3,4} in every row, and column.