ATTENTION, PLEASE READ: The questions is "Does this cryptosystem have perfect secrecy?" Please answer this, show your, and/or provide reasoning. DO NOT FIND ENTROPY.

As an additional reference, attached below is Shannon's Theorem (which I am confident this question is related to). I need a second opinion on this question to check my logic.

Shannon's Theorem:

Consider a cryptosystem in which P-a, b, c), X -{Ki, K2, Ks) and e- 11,2,3,4). Suppose the encryption matrix is as follows: K2 2 3 4 K31341 Does this cryptosystem has perfect secrecy? If IKI ICI IPI then the system provides perfect secrecy iff (1) every key is used with equal probability 1/|KI, and (2) for every x e P and y eC, there exists a unique key k e K such that e(x)y