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\end{pmatrix}.
</math>
Since quaternionic multiplication is noncommutative, care must be taken to preserve the order of the factors when computing the product of matrices.
The [[Identity element|identity]] for this multiplication is, as expected, the diagonal matrix I = diag(1, 1, ... , 1). Multiplication follows the usual laws of [[associativity]] and [[distributivity]]. The trace of a matrix is defined as the sum of the diagonal elements, but in general
:<math>\operatorname{trace}(AB)\ne\operatorname{trace}(BA).</math>
Left scalar multiplication is defined by
:<math>(cA)_{ij}=cA_{ij}.\,</math>
Again, since multiplication is not commutative some care must be taken in the order of the factors.<ref>Tapp pp. 11 ff. for the section.</ref>
==References==
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