I need to show that we have an algebra homomorphism $\phi: M_n(K)\otimes_KA \simeq M_n(A)$ Where A is a K-algebra and K is some field.
I suspect it's really easy but I don't know what to do. Is $\phi$ the homomorphism that sends each entry $(k_{ij})$ of $M_n(K)$ to $k_{ij}a$ or something?