  Complete solutions of functional identities $\sum_{k\in K}F_k(\bar{x}_m^k)x_k
= \sum_{l\in L}x_lG_l(\bar{x}_m^l)$ on the matrix algebra $M_n(\mathbb{F})$ are
given. The nonstandard parts of these solutions turn out to follow from the
Cayley-Hamilton identity.
