Matrix multiplication/Associativity/Exercise

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

Create a solution