So if i've got a non invertible matrix A, (ie, detA=0)

A is in M_K(F) where F is a finite field.

This matrix is used to encrypt vectors a which are in F^k by

c is congruent aA mod n where both c and a are vectors.

Prove that every received vector c can be deciphered as coming from at least two different plaintexts.

Also explain how to provide a precise count of how many different plaintext vectors a are enciphered as the same vector c.

Sorry for my lack of latex skills.