Isomorphisms of the tensor product of $\mathcal{A}^N$

Question

Let $\mathcal{A}$ be an algebra and define $\mathcal{A}^N:=\mathcal{A}\oplus\dots\oplus\mathcal{A}$.

I need to show that

1. $\mathcal{A}^N\otimes_\mathcal{A} \mathcal{A}^N\cong M_N(\mathcal{A})$
2. $\mathcal{A}^N\otimes_{M_N(\mathcal{A})} \mathcal{A}^N\cong \mathcal{A}$

I tried to find an algebra-isomorphism for 1. but failed. I would expect the conclusion that 1. implies 2., but I am not sure how that really follows.

Thanks for your help.