Hill Cipher the point of a known plaintext attack question

Question

Is the point of a known plaintext attack on a Hill Cipher to get the matrix key?

Answer 1

Indeed. If the matrix is $n$ by $n$, and you have $n$ many known plaintext blocks with corresponding ciphertext, you get $n^2$ linear equations in $n^2$ unknowns (the matrix elements) (modulo the alphabet size), which very often can be solved uniquely.