Figuring out key in hill cipher (chosen-plaintext attack)
Sure.  Assuming that you're using the encoding $A = 0$, $B = 1$, etc., just choose your plaintext messages to be the one-block strings:

$$
BA \dots A \\
AB \dots A \\
\vdots \\
AA \dots B
$$

The encryptions of these strings will then directly give you the columns of your key matrix.