Autosomal Inbreeding Probability Matrix

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We are mating two people with Aa genotypes. So the punnet square tells us their offspring will be AA, Aa, or aa with probabilities .25, .5, or .25, respectively. We are interested in breeding these offspring (we are assuming there are many offspring) together and need to find the probability we pair together (AA,AA), (AA,Aa), (AA, aa), (Aa,Aa), (Aa,aa), (aa,aa). My attempt was to multiply the P(AA)*P(AA) and so on down the list but the six probabilities did not add up to 1, as it should. any help is appreciated. this is for a film project for my linear algebra II class. thanks.