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Left scalar multiplication is defined by
:<math>(cA)_{ij}=cA_{ij}, \qquad (Ac)_{ij}=A_{ij}c.\,</math>
Again, since multiplication is not commutative some care must be taken in the order of the factors.<ref>{{cite book |title=Matrix groups for undergraduates|first=Kristopher|last=Tapp
|publisher=AMS Bookstore|year=2005|isbn=0-8218-3785-0 |pages=11 ''ff''
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