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:<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>
==Determinants==
There is no natural way to define a determinant for quaternionic matrices so that the values of the determinant are quaternions. Complex valued determinants can be defined however. The quaternion ''a'' + ''bi'' + ''cj'' + ''dk'' can be represented as the 2×2 complex matrix
: <math>\begin{bmatrix}a+bi & c+di \\ -c+di & a-bi \end{bmatrix}.</math>
This defines a map Ψ<sub>''mn''</sub> from the ''m'' by ''n'' quaternionic matrices to the 2''m'' by 2''n'' complex matrices by replacing each entry in the quaternionic matrix by its 2 by 2 complex representation. The complex valued determinant of ''A'' is then defined as det(Ψ(''A'')). Many of the usual laws for determinants hold, in particular an ''n'' by ''n'' matrix is invertible exactly when its determinant is nonzero.
<ref>Tapp pp. 31 for the section.</ref>
==References==
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