Matrix multiplication is commutative when both matrices are diagonal and of the same dimensions, as well as in cases involving scalar multiples. For example, multiplying two diagonal matrices results in the same product regardless of the order, as demonstrated with the matrices provided. This property holds true because the non-zero elements only affect their corresponding positions, leading to identical outcomes. Understanding this concept can help generalize the commutative property to matrices of any dimension. Thus, diagonal matrices are a key case where matrix multiplication is commutative.