A formula for the number of trace equivalent classes for a matrix string of 2× 2 matrices
which is comprised of two different matrices A and B with k A's and n − k B's is
derived. Simulations for traces of matrix products with 2 A's and n B's for n varying
from 2 to10are carried out. A comparison between traces of ABAB and AABB and their
connection to the eigenvalues of individual matrix is discussed. A formula for a special
case is given and a potential application in Statistical Physics is provided.
Key Words: Trace, Matrix Products, Trace Equivalent Class