I would like to show the following isomorphy but not sure how to go about this:

$\mathbb{K}\cong M_{n}(\mathbb{K})$

Also in Blackadar (Operator Algebras, page 171) he states that this isomorphism induces: $B\cong M_{2}(B)$, $M(B)\cong M_{2}(M(B))$ and $Q(B)\cong M_{2}(Q(B))$, which he calls standard isomorphisms.
In the context or the present question, the notation has the following meaning:

• $B$ is a $C^\ast$-algebra,
• $Q$ is the outer multiplier algebra of $B$ (hence $Q = M(B)/B$),
• $M$ is the multiplier algebra,
• $M_{n}(\mathbb{K})$ are $n\times n$ matrices with entries from $\mathbb{K}$, and finally
• $\mathbb{K}$ is the $C^\star$-algebra of compact operators on a separable, infinite-dimensional Hilbert space.

Anyway, I don't know how to show this and cannot find a reference on how to do this. Would be very thankful for a reference, how to do it or even some hint.