A perfect $(2; 2)$-threshold scheme Given a symmetric encryption scheme with $|K| = |C| = |M|$ that provides perfect
secrecy, it is possible to share a secret $s ∈ M$ between two players by giving one
player a key $k ∈ K$ and the other player the ciphertext $c =$ Enc$(k$, $m)$. Show that
this construction results in a perfect $(2; 2)$-threshold scheme.

I don't know how to do this. Would I go down the route of Shamir's threshold scheme?I know since $|K| = |C| = |M|$ provides perfect secrecy then for every choice of $m$ and $c$, there exists a unique key $k$ but can't see if that helps in any way..
You don't need to adress Shamir's, that is just needed for $k&lt;n$. What you do here is along the lines of the proof that OTP is perfectly secure - actually OTP is one example for this (it is not the general case you are given).

Also see Wikipedia the section "trivial secret sharing", which does list elementwise-XOR with a truly random value for the $2,2$ case (also works for $n,n$. There you just choose $n-1$ shares randomly, and calculate the last one).