Matrix/Multiplication/K/Continuity/Exercise

Show that the matrix multiplication

${\displaystyle \operatorname {Mat} _{m\times n}({\mathbb {K} })\times \operatorname {Mat} _{n\times p}({\mathbb {K} })\longrightarrow \operatorname {Mat} _{m\times p}({\mathbb {K} }),(A,B)\longmapsto A\circ B,}$

is continuous.