pattern - Mensa IQ Test puzzle

Just played a Mensa IQ test online (http://test.mensa.no/)

Answers to these two questions elude me.

Could anyone find out the logic of them? I was puzzled & curious for few days.

Answer

First one:

Square + square gives opposite square.

Same for dots - only dot+dot gives opposite dot, otherwise nothing. You could also say it is multiplication for 1 and reverse solution.
So correct answer is D

Second one:

Look at diagonals: 1x3, 2x2, 3x1
1x1, 2x3, 3x2
and 1x2, 2x1, 3x3 = ?
Only one that could fit is E, since there is always only one change. Like one change from 1x3 to 2x2, one change to 3x1 and so on.