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Is it possible to join matrices in to a bigger matrix?

I have two symbolic $2 \times 2$ matrices $A$ and $B$. I want to join them into a $4 \times 4$ matrix of the form $\begin{pmatrix}A & B \cr B & A\end{pmatrix}$.

The problem is that when I give


I get a three dimensional object, not a four by four matrix. The actual matrices I am working with are bigger than this, so I don't want to do it by hand. Is there a way of doing this without a bunch of for loops?