Matrix multiplication/Composition/Fact/Proof/Exercise

Let ${}B$ be an ${}n\times p$-Matrix, and ${}A$ be an ${}m\times n$-matrix. Let

$K^{p}{\stackrel {B}{\longrightarrow }}K^{n}{\stackrel {A}{\longrightarrow }}K^{m}$

denote the corresponding linear mappings. Show that the matrix product ${}A\circ B$ describes the composition of the linear mappings.

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