# Matrizenmultiplikation/Assoziativität/Aufgabe/en

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Show that the multiplication of matrices is associative. More precisely: Let ${\displaystyle {}K}$ be a field and let ${\displaystyle {}A}$ be an ${\displaystyle {}m\times n}$-matrix, ${\displaystyle {}B}$ an ${\displaystyle {}n\times p}$-matrix and ${\displaystyle {}C}$ a ${\displaystyle {}p\times r}$-matrix over ${\displaystyle {}K}$. Show that ${\displaystyle {}(AB)C=A(BC)}$.