Modeeling Genotype With Matrices

Suppose one parent of some individual is unknown and the other is a hybrid. Their offspring is mates with another hybrid. If this procedure is continued, what is the genotype of the offspring in the long run?
A given genotype is either dominant with genotype AA, hybrid with genotype Aa or recessive with genotype aa. Offspring inherits one gene randomly from each parent. One parent has dominant genes, with genotype AA. The possibilities are:

Parent 1 Type AA\Parent 2 Type AA	A	A
A	AA	AA
A	AA	AA

Parent 1 Type AA\Parent 2 Type Aa	A	a
A	AA	Aa
A	AA	Aa

Parent 1 Type AA\Parent 2 Type aA	a	A
A	aA	AA
A	aA	AA

Parent 1 Type AA\Parent 2 Type aa	A	A
A	Aa	Aa
A	Aa	Aa

We do not know the genotype of parent 2, so consider each table as equally likely.>br /> If the unknown parent has genotype AA, the probability of the offspring having genotype AA is 1/2.
If the unknown parent has genotype Aa, the probability of the offspring having genotype Aa is 1/2.
If the unknown parent has genotype aa, the probability of the offspring having genotype AA is 0.
Carrying on in this way we can construct the table

Parent 2 Type\Offspring Type	AA	Aa	aa
AA	1/2	1/2	0
Aa	1/4	1/2	1/4
aa	0	1/2	1/2

We can write as a matrix  .
Solving the equation

Gives the solution    so a quarter of the offspring will have genotype AA, half the offspring will have genotype Aa and a quarter will have genotype aa.