Why individuals with a dominant trait can be both homozygous and heterozygous, and individuals with a recessive trait can only be homozygous.

The dominant gene always suppresses the effects of the recessive. Thus, the manifestation of the trait, which is determined by the dominant gene, occurs even in heterozygous organisms (where there is both a dominant and a recessive gene).
In a heterozygous organism, one of the genes is always dominant and will suppress the second (Aa). An organism with a recessive trait will always be homozygous for this trait, since there will be nothing to suppress the trait – both genes are suppressed (aa)

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